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COFYRKIHT DKPOSIT. 



ESSAYS IN 

PHILOSOPHY AND PHYSICS 



CONSISTING OF ARTICLES 



ON 



The Laws of River Flow, The Functions of Spheric Wedge, Tides by- 
Reflux, Cyclones, Cold Waves, and Tornadoes; Earthquakes and 
Volcanoes, The Birth of a Planet, The Philosophy of Money. 

6 BY 

Df T. SMITH, M. D. 

Former Lecturer on Medical Jurisprudence and Medical Ethic, Uni- 
versity of Louisville; Former Lecturer on Plant Physiology, 
Kentucky School of Pharmacy; Member of Louisville Bar. 
Author of ''Vibration and Life;'' Moot Points in 
Obstetrics; Cause of Decussation of Pyramids, 
etc. 

Nil tarn dificile est quin quaerendo investigari posset. 




RICHARD G. BADGER 

THE GORHAM PRESS 
BOSTON 



Copyright 1912 by Richard G. Badger 
All rights reserved 



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Q.L,-.'^ 



The Gorham Press, Boston, 17. S. A. 



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©C.|,A34339 



PREFACE 

In venturing to send forth to a discriminating and 
critical public this collection of essays, the author is far 
from being unmindful of the boldness of the undertaking. 
The seven essays embraced in this volume and the 
three others published elsewhere, including the one con- 
tained in the companion volume and entitled ' 'Vibration 
and Life, " make up ten separate problems, a majority of 
which, to a notable degree, have for centuries engaged 
the attention and baffled the efforts of many of the 
world's most capable investigators. 

Furthermore, the contentions here advanced are nearly 
all in a great measure subversive of accepted doctrines 
of science. So much is this the case that when all the 
circumstances are considered the author sometimes feels 
impelled to the impression that the conviction that he has 
supplied the true solution of so great a number of age- 
long baffling puzzles, is merely a dream that has possessed 
him. For how could it be possible that so great a num- 
ber of problems of distinct importance, problems many of 
which have engaged the efforts of leading thinkers of the 
race since science first had a history, are still affected by 
material errors, and that a mere amateur with a quite 
limited educational equipment, should be able to point 
out these errors and discover the alternative truth .^^ 

But if this mistrust has imposed timidity, experience 
has not been altogether inducive of disparagement, since 

5 



6 PREFACE 

several of the contentions urged in these articles have met 
with most encouraging approval from sources where ap- 
proval is of notable value. 

Since the first publication of the views here devel- 
oped, Prof. R. A. Millikan of the University of Chicago, 
as I am advised, has adopted in his teaching, the princi- 
ples of equilibrium as set forth in ''The Functions of the 
Spheric Wedge." Prof. T. J. J. See has developed the 
conception of planets and sa,tellites by capture, as sug- 
gested in a previous publication entitled "The Birth of a 
Planet," Dr. J. Whitridge Williams, Professor of Obstetrics 
in Johns Hopkins University, and probably the foremost 
obstetric writer in this country, has given his approval to 
''Obstetric Problems," and Mr. RoUin A, Harris, of the 
United States Coast and Geodetic Survey, has independ- 
ently developed a theory of tides based on rocking move- 
ments of the water in ocean basins, which seems to differ 
only in name from "Tides by Reflux" as developed by the 
author. It was to be hoped that the New Encyclopedia 
Brittannica would have something more satisfying in the 
way of explaining the puzzling phenomena of stream-flow 
than had previously been offered, but the subject re- 
mains nearly as left by the Italian engineer, Paul Frisi, 
nearly two centuries ago. 

It is not believed that any of these articles will be found 
free from error, but it is confidently hoped that they will 
be found to contain enough newly-discovered truth to 
justify their presentation to the consideration of the 
students and thinkers of all countries, notwithstanding 
the fact that library shelves are groaning everywhere 
with the multitude of books. 



CONTENTS 



THE LAWS OF RIVER-FLOW or THE TRUE 
THEORY OF STREAMS 

Introductory — The Beginning of Seas — Polar Under- 
currents — The Genesis of Rivers — Unsolved Problems 
of River -Flow — Why There are Brooks and Rivers — Why 
Stream Channels are Ellipsoidal or Trough-Shaped^ — The 
Limit of Depth — Why Rivers are Deep near the Sea and 
Yet Enter it Over Channel Beds Sloping Upward — Why 
Floating Material Drifts to the Middle of Streams — Direc- 
tion of Drift at the Bottom — Why the Point of Greatest 
Speed in Streams is Beneath the Surface — Why Streams 
are Highest in the Middle — Why Delta Streams Throw 
up Levees Along their Banks — Why Delta Rivers have 
Multiple Mouths — Kinetic Equilibrium in Streams — The 
Value of Curves — Regulation and Regimen of Channels 
— Bodies of the Drowned Drift to the Shore — ^Rising 
of Streams Below Waterfalls — The Assembling of Streams 
— Deductive Proof of the Double-Spiral — The Lesson of 
Experiments — Experiments of Prof. James Thomson — 
Experiments of Major Cunningham — Vital Importance 
of the Principle — Glaciers and Air Streams — Rocks Rise 
to the Surface — Do Glaciers Erode Channels? — Streams 
of Atmosphere — Blizzards and Texas Northers — Practical 
Application of the Theory — Levees — Lateral Outlets — 

7 



8 CONTENTS 

The Gulf Stream— Effect of the Trade Winds— The Flow 
of Water in Closed Channels 18 



II 



THE FUNCTIONS OF THE SPHERIC WEDGE 

or 
THE PHILOSOPHY OF FLUID EQUILIBRIUM 

Introductory — Transmission of Pressure by Spheric 
Wedges — ^Action of Combined Wedges — ^The Perfect 
Wedge — Limit of Intensity of Horizontal Pressure — Why 
a Flattened Tube Becomes Round — Why Soap Bubbles 
and Rain-drops are Spheres — Balancing of Liquids in 
Connecting Chambers — Balancing Columns — ^The Hy- 
drostatic Paradox — The Bramah Press or Hydrostatic 
Press — The Displacement of Fluids — The Bourdon Steam 
Gauge — ^Relation of the Principle to Isostasy — Production 
and Dissipation of Waves — The Flow of Rivers — Wedge 
Action as a Factor of Tides 101 



III 

TIDES BY REFLUX 

Introductory — Newton's Theory — The Distal Tide — 
La Place's Forced Wave Idea of The Dynamic Theory — 
Tides by Oscillation — ^Theory of Tides by Reflux — Tide 



CONTENTS 9 

Mass a Circle — Why not a Forward Tide? — The Mechan- 
ism of the Distal Tides — Distal Tides and Unequal Attrac- 
tion — Revolution About Common Center — Distal Tide 
by Reflux — Tides at the Poles — Tide-Raising Power of 
Sun — Mechanism of Reflux 145 



IV 

CYCLONES, COLD WAYES AND TORNADOES 

Introductory — Why Cyclones Rotate — Origin of Cy- 
clones — Locality of Origin — Sources of the Energy of Cy- 
clones — The Movement of Progression — Unequal Rising 
of Cyclone Mass — Axis and Center of Gravity — Why 
Cyclones Recurve from Continents — Why Cyclones Avoid 
Mountain Ranges — The Cold Wave, High or Anti-cyclone 
— The Tornado — Formation of Hailstones 171 



EARTHQUAKES AND VOLCANOES 

Introductory^ — Predisposing Forces — The Beginning of 
the Seas — Theories Examined — Theory of the Author — 
Production of Earthquakes and Volcanoes — Volcanic Ex- 
plosions — The Hollow Dome — Long Distance Earth- 
quakes — Magnetic Transference 201 



10 CONTENTS 

VI 

THE BIRTH OF A PLANET or A CRITICISM OF 
THE NEBULAR HYPOTHESIS 

Introductory — Facts in its Favor — Difficulties of the 
Hypothesis — Orbit Must Have Been Enlarged — Modifi- 
cation of Sir George Darwin — Suggestion of Captured 
Comets 223 

VII 

THE PHILOSOPHY OF MONEY 

Introductory — ^DiflFerent Kinds of Value — Delegated 
or Representative Value — The Material of Money — 
Money the Denominator and Standard of Value — The 
Dollar and the Dollar- Worth — ^Table of Ratios of Dollars 
to Dollar- Worths in Various Countries — The Law of the 
Disappearance of Gold — ^Ancillary or Credit Money — 
The Future of Prices — The Future of Money — Debase- 
ment of the Coinage 237 



THE LAWS OF RIVER-FLOW 

OR 

THE TRUE THEORY OF STREAMS 



INTRODUCTORY 

Of the investigations of the ancients in regard to the 
movement of fluids, only the report of those of Archime- 
des have come down to our time, though it is highly im- 
probable that one could have reached the exalted station 
in mechanics and physics that he adorned, without the 
stimulus of having others to share the interest he mani- 
fested, and thus encourage him in his chosen pursuits. 

After the time of Archimedes many centuries passed 
during which not a word of all the records that have 
reached us, reveals that men even thought of theories of 
stream-flow as a matter worthy of investigation. Hydro- 
mechanics must then be regarded as a modern science 
which virtually owes its existence to the great men who 
adorned the seventeenth and eighteenth centuries, and 
Italy may be said to have been its birthplace. Every 
point connected with the theory of torrents and rivers, the 
conducting and distribution of water, the inclines, the 
directions and the variations of channels, were sedulously 
inquired into in that country by Castelli, Viviana, Torri- 
celli, Zendrini, Manfredi, Guglielmini and Frisi. 

The study was really inaugurated by Galileo, the father 
of modern astronomy. He was followed by Castelli and 
Torricelli, two of his distinguished disciples, who, stimu- 
lated by the great interest the question of rivers has for a 
country so dependent on irrigation, and at the same time 
so hable to disasters by floods as Italy, attempted to apply 

13 



14 INTRODUCTORY 

to rivers the principles enunciated by their great master. 

Gughelmini, in a publication made in 1686, came very 
near reaching the position maintained in the present 
treatise, having come to the conclusion that the retarda- 
tion of streams and the regulation of their movement are 
due to transverse currents at the bottom, caused by fric- 
tion against their rough beds. But Mariotte, an eminent 
French authority, having ascertained by experiment, 
that streams are likewise retarded in channels made of 
smooth glass, Guglielmini abandoned his position and in 
a subsequent edition of his works tried to account for the 
phenomena on other grounds. 

Father Grandi also recorded observations in which he 
had seen stones carried out transversely against the 
banks of streams. When the transcendent genius of 
Newton flashed upon the world like a new star in the 
firmament of science and philosophy, that master mind 
deemed the subject of stream-flow not beneath his atten- 
tion. He spent considerable time in its investigation, and 
even devoted a part of the Principia to problems relating 
to the movement of fluids in tubes and open channels, 
but failed of their complete elucidation. 

Since his time a multitude of able investigators have 
taken their turn at the elusive puzzle. Experiments in- 
numerable have been made, and at least three sets of 
these, namely, those of Captain Gordon on the Irawaddi, 
Major Allan Cunningham on the Ganges Canal, and 
Darcy and Bazin at Paris, all backed by their respective 
governments, make reports of more than two thousand 
pages each. Major Cunningham alone made forty thou- 
sand gaugings and experiments. 



INTRODUCTORY 15 

Prof. James Thomson, worthy brother of Lord Kelvin, 
and a man of the highest rank of learning and ingenuity, 
has given the subject of stream-flow extensive study, while 
Forbes and Tyndall have investigated the movement of 
glaciers. 

In France the study of streams has been diligently 
prosecuted for nearly two centuries by such eminent men 
as Mariotte, already mentioned, Pascal, D'Alembert, 
Dubuat, Bossut, Bernoulli, Boileau, Darcy and Bazin. 
In our own country, Captain Eads and Humphrey and 
Abbott are among the most prominent of the students of 
streams. 

It was not, however, by utilizing the observations, ex- 
periments and calculations of others, that the author 
reached, what he is entirely confident, is the true solution 
of the problem of stream-flow; for until he had substan- 
tially completed his theory, which was in 1882, he had not 
read a word of any authority on the subject, insofar as 
now remembered. 

He was first set to thinking on the subject as the 
result of a schoolboy adventiu-e. In the early spring 
of 1858, on an uncomfortably cold day for the season, 
the author and a fellow-student went swimming in the 
Ohio near Brandenburg, Kentucky, as the outcome of 
a banter. His companion took a plunge bath and then 
withdrew. But he, himself, having rolled a treelap into 
the river, tied his shoes to one of its branches and pro- 
ceeded to fioat down stream, with the intention of swim- 
ming ashore after a short time and walking back to the 
starting point. But after drifting a while he perceived 



16 INTRODUCTORY 

that he was gradually being borne away from the bank, 
and he then made an effort to loose his shoes. Failing 
in this because the strings had become wet and a loop had 
slipped, he, just in time, bethought himself to tear them 
loose and having done so started to swim ashore. By 
this time he had drifted so far out into the river, that 
chilled as he had become, he found difficulty in reaching 
the land. 

Naturally the inquiry arose, "Why did the treelap 
drift out into the river .^" and many a time in after years 
the question recurred. Thenceforth, wherever opportu- 
nity offered, the movements of streams, large and small, 
were scrutinized with a view to finding an answer. Step 
by step a little headway was made, until finally a few 
years' residence on the banks of the Mississippi supplied 
an opportunity for a completion of the theory which in 
the fullest confidence of its correctness is here presented. 



THE LAWS OF RIVER-FLOW 

OR 

THE TRUE THEORY OF STREAMS 

When the earth is contemplated as a dwelling-place 
for man, its fitness in this regard appears to bear a vital 
relation to the behavior of the streams of water that fur- 
row its surface. 

But before these came the oceans exhaling vapor into 
the air to be gathered later into clouds and then cast down 
as rain or snow. The water, when precipitated from the 
clouds, at first collected into diminutive bodies each of 
which proceeded to carve out for itself a channel along 
which it found its way to a river, or the sea, presenting 
in course of time an altogether pleasing alternation of 
quiet pools and rippling shallows. This arrangement 
renders all but the very smallest of streams fit homes for 
a teeming life which, while reveling in a joyous existence, 
in turn serves as food for man. 

Gathering later into rivers, the collected water sought 
the great ocean reservoirs, whence under the wooing of 
the sun it again and again returned to revive the parched 
land, to make the earth glad with tree and flower and 
fruit and waving grass, and to gather therefrom a gener- 
ous impost wherewith to sustain the various tribes to 
which the glassy deeps give shelter, and to carry back 

17 



18 SMITH'S ESSAYS 

a grateful tribute to feed the innumerable denizens of the 
ocean. 

In what way these rivers, rivulets and seas, that not 
only contribute so freely of useful service to the inhabi- 
tants of the earth, but also have chiseled every feature 
of beauty presented by its surface, have themselves been 
brought into existence and to what laws and regulations 
they are obedient, is a subject worthy of the most patient 
and diligent inquiry. 

It is under the conviction that new light may be shed 
upon the character of the mechanism and the nature 
of the laws which have been employed and observed in 
their production and control, that the author has felt 
emboldened to offer the views embraced in the present 
effort, firmly confident that a baffling secret of centuries 
has been revealed. 

The Beginning of Seas 

Before the erosion of rivers could be inaugurated, the 
gathering of the waters into seas and oceans had to be 
accomplished, and the separation and elevation of the 
dry land. 

As soon as the incandescent mass of which the earth 
at one time consisted, had cooled sufficiently to allow 
the clouds of vapor which surrounded it to condense and 
reach its surface in the form of water, the areas where the 
waters fell first and most abundantly, lost their heat more 
rapidly than other portions of the surface. 

The areas so cooled also contracted more rapidly and 
acquired thereby a greater specific gravity than the sur- 



THE LAWS OF RI\^R-FLOW 19 

rounding and hotter superficial mass or crust: and being 
thus weighed down by the water that accumulated upon 
them as a result of their depression, they sank still further 
into the liquid mass, as a partly filled bowl would sink into 
a vessel of water. 

Since the polar regions must have been the part of the 
earth's surface first to have its temperature thus reduced, 
the beginning of the seas must have been in the neighbor- 
hood of the poles. As the cooling of the earth progressed, 
the areas of sea formation increased in extent until it 
finally became possible for water to remain on the entire 
surface. But until a solid crust of considerable thickness 
was formed, there must have been, from a multitude of 
causes, an almost continuous shifting of the surface level. 

Thus different rates of heat radiation from the earth's 
surface, deformation due to the attraction of the sun and 
moon, and even to a slight extent, that of other heavenly 
bodies, as well as varying chemical combinations, and 
especially the winds must have resulted in more or less 
disturbances of level. 

Polar Under Currents 

After the sea had attained a considerable depth, and 
the thickening earthcrust had been m^ore or less perma- 
nently divided off into dry land and^ocean bed, cold un- 
der currents set in from the direction of the poles, and the 
earth at the bottom of the seas cooled off still more rapidly 
than before, and also still more rapidly than the elevated 
or dry land. For, aside from the influence of the polar 
undercurrent, water is a more effective agent in extracting 
and dissipating heat than the atmosphere. 



20 SMITH'S ESSAYS 

Another effective agency in lowering the specific gravity 
of the elevated lands, and raising that of the material 
forming the bottom of the seas, has probably been the 
continuous filtering of the various salts from the elevated 
lands and their transference to the ocean bottoms. 

For, as the bed of the ocean by its subsidence, gradually 
forced upward and above its own level the dry land, water 
derived from rain and snow, has steadily percolated the 
land everywhere, dissolving out vast quantities of soluble 
substances and carrying them to the sea, both by way 
of the rivers, and of that great subterranean movement 
of seepage, that is continually going on in the direction 
of the ocean. 

This process has left the dry land more or less honey- 
combed throughout and of diminished specific gravity. 
On the other hand, of this extracted matter, the soda and 
magnesia salts alone seem to have remained in solution in 
the water of the ocean in any considerable quantity or 
proportion. Nearly all the others settled down and be- 
came incorporated into the rocks that form the bottom of 
the seas and by so much added to the density and 
weight of the ocean floor, and thus increased its sub- 
sidence. 

Still another and important factor in diminishing the 
specific weight of mountains is the expansion of their con- 
stituent elements while in the act of rising above the com- 
mon level, wherever these elements consist in considerable 
part of lava. Whatever might be accomplished by a pent 
up force in expelling lava to great heights, from a mere 
tendency to effect equilibrium, lava could no more rise 
above the common level of the settling crust than water 



THE LAWS OF RIVER-FLOW 21 

could rise above ice that might be floating in it. So if a 
mountain should be lifted up by folding there would be 
produced beneath the folds a vacuum, if the space were not 
filled up by the expanding material beneath in places 
where the segments of the folds lean against and mutu- 
ally support the weight each of the other. 

It is the greater thickness and greater specific weight 
of the earth's crust forming the floor of the ocean, that 
enables it to counterbalance the dry land and produce an 
equilibrium, notwithstanding the fact that though cov- 
ered several miles deep with so light a material as water, 
the level of the ocean surface is still so much below the 
level of the land. 

For from the known laws of equilibrium as applied to 
the earth, or the principle of isostasy, it must result that 
two cones of equal angle, taken the one from the deepest 
sea, and the other from the highest mountain plateau, 
with their apexes resting at the center of the earth, must 
be of equal weight. 

It is certain, however, that there are other but unknown 
forces at work determining the alternate rising and falling 
of the earth's surface. All the known geologic forces at 
work make for stability and permanency, all tend to 
deepen the seas and to elevate the land. And yet the 
major part of the earth's surface that has been examined 
is known to have been again and again by turns submerged 
and raised above the level of the water. 

How this has come about, except insofar as can be ac- 
counted for by the depression produced by sedimentary 
deposits, no one professes or pretends to know: nor has 
even a guess, so far as can now be recalled, been ventured 
in explanation. 



22 SMITH'S ESSAYS 

Is it barely possible that the great earth currents of 
electricity, that determine the magnetic poles, could by 
cataphoretic action beneath the earth's surface, shift vast 
metallic masses from one region to another, and in this 
way bring about the successive rising and subsidence of 
the crust? 

If a still wider digression than the next preceding may 
be excused, it might be suggested that the operation of 
the mechanism just considered, viz.: the subsidence of 
the ocean bed and the resulting elevation of the land is, 
in a way not hitherto considered, probably the chief factor 
in the production of volcanoes, especially the more vio- 
lent ones, and also largely a factor in the production of 
earthquakes. 

The chief determining mechanism in both earthquakes 
and volcanoes is the lateral pressure of the thick and 
rigid sea-bottom crust against the more yielding dry land 
crust. This may be realized in a very simple experiment. 
Thus, if a piece of cardboard and a sheet of letter paper 
be pressed edgewise against each other, the thin paper will 
bend before the cardboard: and if they rest on an unyield- 
ing surface the convexity of the bend in the thin paper 
will be directed upward, and close to the edge next to the 
cardboard. In like manner when the strong and rigid sea- 
bottom crust is pressed edgewise against the lighter and 
weaker dry-land crust by the force of the earth's shrinkage, 
there occurs at the junction of the crusts, such a bending 
as produces two curves: one with a convexity downward, 
at the level of the ocean bottom, and the other with an 
upward convexity, in the landcrust near the seashore. 
With every increase in the contraction of the earth, these 
curves must of course become sharper. 



THE LAWS OF RI\TER-FLOW 23 

Every increase in the convexity of the curve in the sea- 
bottom crust, will tend to produce fractures resulting in 
the formation of inverted V-shaped fissures in its under 
surface. 

These in the great majority of cases will be very small, 
in others they will extend deep into the crust. Occa- 
sionally when the line of fracture passes through a great 
trough-like depression as in abysmal deeps, the upper 
edges of the rim of such trough will act as a fulcrum or 
brace and in this way the fissure will be made to extend 
quite through the crust up to the water above. 

On the other hand, every increase in the upward con- 
vexity of the land crust will result in fractures producing 
V-shaped fissures in its upper part : sometimes only super- 
ficial, and at others extending quite to the incandescent 
mass beneath. 

Into these inverted V-shaped fissures when thus formed 
expansible material from the compressed incandescent 
mass of the earth's core will escape, and rushing against 
the walls of the fissure, will give rise to a shock of corres- 
ponding violence. 

At other times, when these fissures extend entirely 
through the crust and up to the bottom of the ocean, the 
water with the force of several miles of pressure from the 
overlying mass, will rush down with tremendous speed 
and force, and meeting on its vv^ay the glowing lava rising 
up from below, will be suddenly changed into vapor. 

But the vent at the apex of the fissure will now be 
found too small to allow the steam to escape, blocked as 
it is by the water perhaps miles deep above it, that must 
be moved by explosive force, with the overcoming of the 
tremendous inertia of the water this implies. 



24 SMITH'S ESSAYS 

The result will sometimes be that the pent-up forces 
will make their way along the easier route, up under the 
dome constituted of the leaning earth crust to the V-shaped 
fissures in the dry-land crust, and escaping thence, pro- 
duce volcanoes. Or, in exceptional cases, where very 
large masses of water find their way into fissures extend- 
ing quite through the crust, there may occur a cataclysmic 
explosion, such as that which blew to pieces Mount 
Krakatoa in the straits of Sunda. 

It is well to note that while the earth crust is bending 
upward at the margin of the sea, its weight must thereby 
be partly lifted from the incandescent mass beneath, and 
it may also be noted that even if the crust which forms the 
ocean floor, is no thicker nor denser than the land crust, 
but only equally as thick, it must still, other things being 
equal, be rendered more rigid by reason of the weight of 
the ocean water resting upon it : that is to say, it will bend 
less easily than the dry-land crust. 

The Genesis of Rivers 

Having thus briefly considered the preparation of the 
earth for the movement of water on its surface, we may 
now pass to an investigation of the definite mechanism by 
which the water has been gathered into channeled streams 
together with the many interesting characteristics with 
which these are endowed and by which they are distin- 
guished. 

x\s soon as the level of the seas became sufficiently 
lower than that of the dry land, drainage began from the 
surface of the elevated portions, and initiated the forma- 



THE LAWS OF RI\^R-FLOW 25 

tion of streams, a part of which ultimately became rivers. 

These grew with the widening continents through the 
long eons of time, and when man appeared upon the scene, 
they must from the earliest unfoldings of intelligent curi- 
osity, have been among the chief features of the landscape 
in lending interest and charm to his dwelling-place. They 
probably yielded at first his main supply of animal food. 
They formed one of the earliest and often one of the easiest 
means of intercommunication, as well as the natural boun- 
daries of the political or tribal divisions of territory. And 
when at last the earth began to grow weary of its barba- 
rism, the river and the desert in beneficent wedlock, gave 
birth to civilization, and with rich provision of fruit and 
grain nourished it into strength. 

Thus it most naturally came about that in many lands 
rivers, in recognition of their beneficent influences and 
their wealth of charm, were chosen as objects of divine 
adoration. Nor have they yet ceased to supply the paint- 
er with an exhaustless theme for his pencil, the poet with 
a perennial and generous inspiration for his verse, and 
the philosopher with food for profound contemplation. 

Sustaining so many important relations to the happi- 
ness and well being of mankind, adding so much of charm 
to his dwelling place, filling so many offices of usefulness, 
and necessarily present and operative as a living force 
in every habitable region, it is not strange that rivers 
have been through all ages, objects of lively and curious 
regard, as in more recent times of sedulous philosophic 
research. 



26 SMITH'S ESSAYS 

Unsolved Problems of Riverflow 

In the course of the centuries of investigation into the 
laws of streams, many interesting problems have arisen, 
having a bearing on their origin and behavior. Yet not- 
withstanding the world-wide presence of rivers, and the 
incentive that has drawn to their study so many of the fore- 
most physicists of modern times, a majority of the prob- 
lems of stream-flow remain to this day confessedly with- 
out solution and many striking phenomena remain wholly 
unexplained. 

Included in this category, the following questions pre- 
sent themselves as entirely unanswered, although they 
embrace a decided majority of the problems of philosophic 
interest relating to the flow of liquids in open channels. 

They offer the test and the criterion by which any doc- 
trine of streams must be tried and passed upon: for with 
the principles and phenomena they indicate, any true and 
consistent theory of streams must accord. 

First: Why are there brooks and rivers and by what 
mechanism has water been enabled to carve out channels 
in masses of solids having a specific gravity two and a half 
to five times greater than its own? 

Second: Why are the channels of streams trough- 
shaped, or ellipsoidal in form.^ 

Third: What causes produce the observed succession 
of deeps and shallows in streams, and limits their depths, 
and why do the channel beds of streams rise as they enter 
the sea.f^ 

Fourth: Why does floating material drift from the 
margins to the middle of streams? 



THE LAWS OF RIVER-FLOW ^7 

Fifth: Why is the swiftest point or locus of greatest 
speed in streams, not at the surface, but at a considerable 
distance beneath? 

Sixth: WTiy are streams higher in the middle than at 
the margins? 

Seventh: Why do rivers flowing through their deltas, 
throw up ridges of earth or natural levees along their 
banks? 

Eighth: W^hy do rivers entering the sea through deltas 
of their own deposit, have multiple mouths? 

Ninth: Why does water moving in channels, attain 
less speed in proportion to the increase of channel incline, 
than do soKd bodies under like conditions? 

Tenth: What is it that determines the tendency of 
streams, both surface and underground, to gather into 
larger channels, even to the forsaking of established chan- 
nels? 

The correct answer to each and all of these questions, 
which embrace practically the entire field of stream- 
activity, the author is firmly convinced, is to be found 
in the right interpretation of a principle that underlies 
the movement of all liquids as well as fluids which he be- 
Keves he has discovered and which he has ventured to 
denominate '*The Law of the Double Spiral." 

We will now proceed to develop this principle and to 
test its truth, applying it successively to the solution of 
the various problems embraced in the foregoing category. 

Why There are Brooks and Rivers 

In order to elucidate the principle upon which the con- 



28 SMITH'S ESSAYS 

centrated and orderly erosion of channels is based, let us 
begin with the investigation of a stream in the first steps 
of channel formation. For this purpose we may suppose 
a quantity of water to be steadily and continuously poured 
upon a smooth stretch of erosible material, with a plane 
surface of suflficient incline to determine the flow of the 
liquid. Furthermore, we may consider the resulting stream 
of water as consisting of columns of molecules, extending 
perpendicularly from the top to the bottom. 

At first the water will move down the incline in a thin 
stratum, limited and restrained on either side by a wall 
held together by that form of adhesion known as surface 
tension; just as a drop of water on a floor, will stand out 
inclosed in a wall of its own particles, and in a measure 
retain its spheric form. 

In the stream assumed to be formed in this way, the 
column of molecules at the outer edge on either side and 
next within the walls, will be retarded more than any of the 
other columns further in. And since friction at the bottom 
must be greater than at the top, this will cause the mole- 
cules at the lower extremity of the external columns on 
either side to be most retarded of all the particles. 

Not only will these lowest and outermost molecules be 
most of all retarded, but the retardation will be continuous 
and progressive. Therefore, if they do not from some 
source receive a new impulse from time to time, they will 
eventually of necessity come to a complete standstill. 
Friction against these arrested molecules will then cause 
the next within to come to a stand, and so on until the 
entire stream becomes involved in the retardation and it 
ceases to flow. 



THE LAWS OF RIVER-FLOW 29 

It is not to be presumed, however, that the rows or 
lines of molecules follow each other in this situation and 
in this order, that is to say the row of molecules nearest to 
the bottom and nearest to the edge will not be uniformly 
retarded even in the smoothest channels; for absolute 
smoothness of molecular movement is never realized 
except in the concepts of mathematics. 

These molecular stream lines will be pulled apart and 
broken times innumerable : but as the stream must convey 
an undiminished quantity of water as it progresses on its 
journey, it is indispensable that its sectional area be pre- 
served intact. 

Therefore, whenever a break begins to occur in the out- 
ermost line of molecules and threaten the narrowing of 
a stream, that is whenever a gap begins to form in this 
outer line, or lamina, it must be reenforced or filled in 
from the faster moving column of molecules next within; 
and this if for no other reason than that there is none on 
the outer side from which it can be supplied. 

Owing to the fact that the degree of friction progressively 
and proportionally decreases in the direction of the middle 
of the stream, each column in the direction of the middle 
^dll have a greater speed than the one next outside of it: 
and from whatever part of such column the substitute 
molecules or molecule may be taken, they will be moving 
faster than the ones they may have supplanted. 

If a rod be thrust into a body of water, however deep, 
and then instantaneously withdrawn, the hole thus made 
would fill first from the bottom. likewise when there 
occurs an incipient vacuum at the bottom of a retarded 
external column, this column will not settle down to sup- 



30 SMITH'S ESSAYS 

ply or fill it, but it will be supplied from the bottom of the 
next column within. 

Again, as entire columns next to the wall become re- 
tarded, the tendency will be for entire columns next within 
to take their places; but the tendency would be stronger 
at the bottom than at the top, and the water would move 
out with greater momentum at the bottom than at the top. 
The result of this would be that the molecules at the bot- 
tom of the outer column would be driven out of the 
way, and as there remains now only one direction in which 
they can move, they must take that direction and be lifted 
upward. 

The third column from the bank will in turn treat the 
second in the same way: and this process will continue 
until the middle of the stream is reached from either side. 
When the stream has been equally divided on the basis of 
retarding forces, and the middle has been reached from 
both sides by this outward movement at the bottom, the 
molecules or masses displaced, either by further retarda- 
tion or by the outward movement below, must be replaced 
from above. This will produce a constant settling down 
of the water in the middle of the stream, along the line of 
its current. 

In the meantime the outward movement at the bottom 
of the stream, will be attended by a momentum propor- 
tional to its speed, and the eflPect of its impact will be to 
lift up the water along the margin into a border or ridge. 
As a result of this elevated border being formed along both 
of the stream margins, the surface of the stream will on 
transverse measurement exhibit the form of a trough. 

Having now in the case of the smallest stream sought an 



THE LAWS OF RIVER-FLOW 31 

illustration of the molecular movement of flow, we will 
next take up the consideration of a larger type of stream, 
with a view to an easier comprehension, and we will sup- 
pose such a stream to have reached the stage where the 
water has been heaped up at the margins into a border by 
the outward movement below. 

The surface of the stream now exhibits an elevated 
border along each margin, and a longitudinal depression 
along the middle, constituting it a veritable trough. Each 
half of this trough will have a surface sloping in two direc- 
tions, one toward the depressed middle line of the stream, 
and the other downw^ard in the line of the axis of the 
stream-bed or channel. 

The water which has been heaped up at the banks by 
the impact or momentum of the outwardly flowing under- 
currents will tend at the same time to flow transversely 
from the elevated border to the middle, and longitudin- 
ally in the direction of the stream axis. As a resultant 
the flow will be obliquely inward toward the middle and 
downward in the direction of the stream axis. At the 
same time, the water having been drawn away from the 
middle of the stream at the bottom, one-half toward each 
of its banks, this incoming water of the surface will sink 
down through the middle to take its place. 

In obedience to these forces, therefore, every stream 
moving in a channel consisting of firm material, of necessi- 
ty resolves itself into two equal cylinders or trapezoidal 
bodies which revolve or shear over spirally on parallel 
axes in opposite directions: that is, outward at the bottom, 
upward at the margins, inward at the top and downward 
through the middle. 



32 



SMITH'S ESSAYS 




TRANSVERSE SECTION OF STREAM. 

A — Elevated middle of stream. 

B — Locus of greatest speed. 

C — Center of cylinder. 

The arrows show the direction of the spiral motion. 



A very casual consideration of the subject will render it 
quite obvious that some such method for effecting the 
concentration of flow is indispensable to the erosion of 
channels. If, as commonly held to be the case, water in 
streams moves along in filaments or layers, one gliding 
over another, the formation of channels could never be 
the outcome of such an arrangement of movement. 

In such case, scour could be effected only by the bottom 
layers, and these after a brief period, would become laden 
to the limit with silt. And since the mountain streams 
would take up and bear along a greater quantity of silt 
tha^ the lower strata of the streams of the plains could 
carry, the tendency would be to deposit it on reaching the 
valleys, and the effect would be rather to fill up than to 
scour out channels. 

Nor is there reason to believe that on any principle 
hitherto suggested, water would tend to the formation of 



THE LAWS OF RIVER-FLOW 33 

channels. No reason can be given, derived from any of 
the present teachings of science why running water should 
not spread out over the land indifferently, and make its 
way in a wide, thin sheet, by a slow, creeping movement, 
to the sea, instead of carving out channels and traveling 
in them. 

The explanation ready to the mind of the casual ob- 
server is, that rivers are formed by reason of the water 
seeking the lowest constructional depressions. 

But this explanation, at first blush so plausible that it 
seems fairly self-evident, fails completely when we exam- 
ine the rivers of deltas, or rivers that have reached the sea 
through accumulations of silt of their own depositing. 

In such situations it will usually be found that the rivers 
or their various mouths, or passes, have actually carried 
detritus out into the sea, and walled off the sea water by 
building banks for themselves and making their own chan- 
nels. Along the outlets of the Mississippi, and doubtless 
the outlets of all other delta rivers, one may travel for 
considerable distances on boat through the passes, so 
near to the sea walled off on either side by the action of the 
river, that he may throw stones into it across the narrow 
banks that reach out into the waters of the gulf like so 
many fingers. 

Why Stream Channels are Ellipsoidal or Trough- 
shaped 

It is obvious that after the water of the upper part of a 
stream leaves the bank to begin its flow toward the mid- 
dle, its speed continues to increase by reason of the relative 



34 SMITH'S ESSAYS 

lessening of friction, not only till it reaches the point 
where it must change its direction obliquely downward 
toward the bottom, but also until it has passed for some 
distance below the level of the surface. The force of 
collision of the masses of water coming from the two sides 
of the stream, must also have some effect in the way of 
accelerating the flow. 

The water of the most rapid part of the stream, there- 
fore, has the most direct course toward the bottom, and 
consequently in the line of this part, which is also the 
line or axis of the current, the greatest extent of scour or 
erosion must take place. Every stream then, other things 
being equal, must be deepest in the line of its current. 

The water passing down from the surface as already 
indicated, continues to gain in speed until it traverses 
about three-tenths of the distance to the bottom. At 
this point it begins to suffer the retardation due to the 
frictional resistance of the bottom of the channel. There- 
fore when it reaches the bottom its speed is nearly the 
same as, or even less than, that of the surface. 

This retardation steadily and progressively increases 
during the time that the water at and near the bottom 
is moving obliquely outward toward the banks, and the 
erosion of the channel diminishes proportionally with 
the retardation of the speed of the flow. 

At last the speed in the direction of the bank be- 
comes too small for any erosion to take place, whereupon 
the water, rising toward the surface, begins again its 
journey toward the middle. The force and extent of 
this movement must for every stream, determine its 
limits as to width and depth. It is obvious also that 



THE LAWS OF RB^R-FLOW 35 

such a movement must result in the formation of a trough- 
shaped or eUipsoidal channel. 

But the intimate or ultimate movements involved in 
stream-flow, are far more complex than would appear on a 
superficial investigation, and to be fully understood, would 
require an exhaustive investigation of the whole subject 
of fluid equilibrium. 

Even in its grosser aspects, as will be referred to again 
in another connection, water in streams moves in a most 
confusing and irregular way. Diminutive masses are 
being constantly projected inward and outward, upward 
and downward unceasingly. 

Reference has already been made to the retardation of 
the molecules of water at the bottom of streams, with the 
saving explanation that a purely molecular retardation or 
movement is never fully realized: the fine disturbance in- 
variably comes to involve larger masses. The particles 
hitherto spoken of as moving aside toward the bank to re- 
place other particles that a,re falling behind, must them- 
selves become too much retarded to reach the bank by 
traveling along on the bottom. Consequently, after hav- 
ing become aggregated into considerable masses and 
become too sluggish in their movement to be able to 
ascend the sloping channel bed, other masses that have 
moved out from a higher level, that is from a level farther 
from the bottom, and consequently are moving with 
greater speed, strike them with such force as to project 
them upward toward the surface. 

In the deeper portions of the stream this condition, 
though constantly present, will not as a rule be observed 
at the surface. But toward the margins of the stream, 



36 SMITH'S ESSAYS 

these masses moving often from the bottom, or from near 
it, will penetrate the upper and inward moving half of the 
stream, and evidence their presence by a constant boiling 
up of the water, which in muddy streams is quite conspic- 
uous. These boilings are for the most part the result of 
impulses sent from below, and not the identical masses of 
water projected from the bottom. 

As long as these irregularly moving portions come in 
contact only with other parts of the stream mass, they ex- 
pend their momentum in producing widespread and some- 
what uniform disturbance of movement. But when they 
meet with firm resistance, as from a solid bank, the impact 
produces a distinct increase of pressure at such surface. 

Obviously these impacts of pressure in a stream, being 
directed mainly against the channel walls, are an addition- 
al factor, or a feature of the factors, determining the up- 
ward and outward movement along the sloping sides and 
bottom, respectively. 

It is to be borne in mind, that strictly speaking, no typi- 
cally ellipsoidal or trough-shaped channel actually exists in 
nature; yet the shape of every channel eroded through 
homogeneous material, is in the mean ellipsoidal. For, if 
one of the banks presents an abrupt departure from this 
contour the opposite one will have a correspondingly 
gentler slope, and this will compensate for the departure 
of the other from the normal order, or the average form. 

The Limit of Depth 

But there must be forces in a stream operating to deter- 
mine the limit of depth as well as the limit of width. Fur- 



THE LAWS OF RIVER-FLOW 37 

thermore, this force must be self-regulating, otherwise 
streams would go on deepening their channels indefinitely: 
but this is nowhere the case. 

In this connection we may anticipate and consider also 
the formation and regulation of deeps and shallows, or 
pools and rifl3es in streams, since they depend on the same 
principles. 

WTiatever may be the incline of its bed, almost every 
stream consists of a succession of deeps and shallows, and 
under like conditions these bear a uniform relation, both 
in depth and frequency, to the magnitude of the streams 
in which they occur. Wha.t is it then that arrests erosion 
in streams, and why do they not go on deepening indefi- 
nitely.'^ 

The explanation offered by the Italian engineer, Paul 
Frisi, in the middle part of the 18th century, and generally 
accepted in his da}^, was that after reaching an uncertain 
depth, the bottom of stream beds become paved with 
coarse sand and gravel, where they do not already consist 
of rock, and that in this way further erosion is prevented. 
And curiously enough, in the century and a half that has 
elapsed since his day, and up to the present hour, no other 
explanation has been offered, insofar as the writer is ad- 
vised. 

Every one, however, who has made any practical study 
of streams, knows that the facts do not bear out the explan- 
ation. Gravel and sand in creeks, and gravel, sand and 
boulders in rivers, are not found in deep but in shallow 
places and on riflSes. The cause of the arrest of erosion in 
the bottom of streams must then be sought elsewhere. 
Sir Charles Lyell in some reports that have become 



88 SMITH'S ESSAYS 

classic, announced as the result of a series of experiments 
made under his supervision, the rule that water moving 
with a velocity of forty feet per minute, will sweep along 
coarse sand; with one of sixty feet, fine gravel; with one of 
one hundred and twenty feet, rounded pebbles, and with 
one of one hundred and eighty feet, or a little more than 
two miles an hour, angular stones of the size of an egg. 

These experiments have been accepted as authoritative 
by many writers on the subject, and they appear also in 
several encyclopedias. What depth of water was em- 
ployed by Lyell in his experiments or with what shape of 
channels his streams were provided does not appear. Evi- 
dently the experiments were not complete, since they do 
not embrace the larger masses of rock that it is known can 
be moved by floods, and it can probably be shown also 
that they are in other respects misleading. 

In support of the explanation of the phenomena in 
question about to be offered, it becomes necessary not only 
to qualify the results given out by Sir Charles Lyell, 
but also to correct a misapprehension that some other writ- 
ers seem to rest under, which is the notion that the move- 
ment of a body under water is not affected by pressure. It 
is true that skin friction in water is not affected by pressure. 
That is a body practically without thickness will move as 
readily in deep water as in shallow, but this does not 
signify that a mass or body of any considerable thickness, 
will move with as little resistance in deep water as in shal- 
low. 

If the principle were to hold true without qualification, 
the depth of the water would count for nothing in the 
lifting and transporting of any form of detritus. After 



THE LAWS OF RIVER-FLOW 39 

the depth of water should become sufficiently great to 
cover the object to be moved, its transportation would 
become a question of the speed of the water alone. 

But as previously )bserved, sand, gravel and boulders 
are found, not in the deep pools in creeks and rivers, but 
in shallows or on riffles : as a rule it is mud that forms the 
bottom of the deeper pools. It is a matter of common ob- 
servation tha.t if a boulder be cast into a deep poo] in a 
stream when it is low, it will be picked up by the water in 
times of flood, carried to the next shallow further down, and 
there dropped and left in water swifter than that from 
which it has been removed. This frequently happens 
even with stones of large size. 

The erosive power of a stream must then, have a rela- 
tion to the depth of the water as well as 1 3 its speed. This 
may not be and probably is not, directly as the product 
of the speed by the depth, but it is doubtless some regular 
product of those factors. For the purposes of our argu- 
ment we may assume that the relation is direct and con- 
stant. 

In order to obtain a clear apprehension of the process of 
erosion, and the laws to be deduced as controlling it, we 
may conceive the example of a stream occupying a rec- 
tangular canal. It is easy to perceive that if the depth of 
the water at any time moving in such a canal is reduced by 
one half, it will be necessary for the speed to be doubled in 
order that the same quantity of water as before, shall pass 
a given point in the same time. 

If the depth is dimini<=;hed by three fourths, we shall have 
to add three fourths to the speed and so on reciprocally for 
all other proportions. Proceeding then on the assumption 



40 SMITH'S ESSAYS 

that the erosive power of water is the direct product of the 
speed by the depth, we obtain a numerical, or mathemat- 
ical formula, that is entirely consistent with observation. 

In a canal such as we have supposed with a constant 
width and depth, let a be the normal depth and b the normal 
speed. Now any variation of the depth and speed from a 
and b giving the same sum as they do, will give a dimin- 
ished product, whether such variation be the increase of a 
and an equal lessening of b, or an addition to b with an 
equal subtraction from a. 

That is, a multiplied by b will give a larger product than 
will any other two numbers into which the sum of a and b 
can be divided. This can readily be gathered from the sub- 
joined table in which the normal depth and speed are each 
represented by the number four. 

Depth Speed Sum Depth Speed Prod'ct 



8 


+ 





= 


8 


8 


X 








7 


+ 


1 


= 


8 


7 


X 


1 


= 7 


6 


+ 


2 


= 


8 


6 


X 


2 


= 12 


5 


+ 


3 


= 


8 


5 


X 


3 


= 15 


4 


+ 


4 


= 


8 


4 


X 


4 


= 16 


3 


+ 


5 


= 


8 


3 


X 


5 


= 15 


2 


+ 


6 


= 


8 


2 


X 


6 


= 12 


1 


+ 


7 


= 


8 


1 


X 


7 


7 





+ 


8 


= 


8 





X 


8 


= 



From this it appears that if a stream varies in either 
direction from a certain reciprocal relation of speed and 
depth, which may be denominated the normal, erosive 
power or erosive action diminishes finally to disappear 
altogether as zero is reached in either depth or speed. 



THE LAWS OF RI\1SR-FL0W 41 

In the same way that the depth of streams as a whole, 
depends upon the conditions expressed in the foregoing 
formula, the depth of the pools that alternate with shal- 
lows is fixed and determined as has been already indicated. 
The position which these pools hold with regard to each 
other, however, is most probably due to some other modi- 
fying influence. And since we find these pools or deeps 
far apart in the larger, and closer together in the smaller 
streams, we would naturally infer that wave action is the 
controlling force; such wave being probably of the class 
known as the forced wave: or it may be that ill defined 
character of wave manifested in the seiche, and also prob- 
ably to some extent of that of the larger tidal wave both 
manifested as rockings. 

Any one who watches the flow of a stream during the 
flood stage, may observe a kind of longitudinal rocking, that 
might well be supposed to aid, at least, in bringing about 
the observed conditions of the stream bed. But whatever 
it may be that determines the production of deeps and 
shallows, we must in addition to accounting for the arrest 
of deepening in pools, and the general body of streams as 
well, also account for the fact already alluded to, that in 
deeps, masses of heavy material, such as sand, stones, 
boulders and gravel, are picked up by the water during 
floods, carried to the next shallow below and there depos- 
ited. 

The explanation of this fact also will be found in the 
suggested formula. To account for it we may recall that 
during floods, practically the same additional depth is 
added to the deep and the shallow parts of the stream. 
This condition adds relatively more to the speed of the 



42 SMITH'S ESSAYS 

deep water than it does depth to the previously shallow 
water, and as a result, sends the maximum speed — ^point 
downward faster in the deep water than in the shallow. 
It must not be lost sight of that the forces in operation 
in the deepening of streams, whether in deeps or shallows, 
are subject to the regimen established by the next obstruc- 
tion below. Such obstruction may be a rocky barrier 
like those causing falls in rivers, shallows or riffles, or the 
level of the ocean into which the streams empty. 

Why Rivers are Deep Near the Sea and Yet Enter 
It over Channel Beds Sloping Upward 

At or near the mouths of nearly all streams that empty 
directly into the sea, there is found a shallow stretch of 
water or extended bar in the channel near the point of 
entrance while immediately above this bar the water is 
almost invariably deep. The general rule is that rivers 
enter the sea with the bottom of the channel sloping 
upward. 

The cause of the bar at the mouth of the stream, is 
simply the precipitation of silt from the water of the 
river, due to the impeding of its flow on reaching the sea: 
but the deepening of the channel immediately above 
the bar has a different cause. 

When the tide flows in at the mouth of a river the water 
is dammed back and kept nearly on a level with the adja- 
cent sea. As the tide recedes, the sea water retreats more 
rapidly than the water of the river can flow out, and the 
result is a marked slope of the surface of the river where it 
joins the sea. At first only the water in that part of the 



THE LAWS OF RIVER-PLOW 43 

river above the sea-level will participate in the movement, 
the water at greater depths remaining as yet stationary 
and undisturbed. 

This speedily brings about a condition very favorable 
to the development of the double-spiral. For, the head of 
water in the river a short distance up, caused by the out- 
flow of the water in the river near the sea, will quickly 
start the water on the sides of the slope in their upward 
movement, and this will inaugurate a brisk flow, both 
spirally and longitudinally. The result will be the pre- 
cipitate movement downward of the water in the middle 
of the stream and the boring out of a deep place in that 
part of the channel. 

It is, indeed, a question whether there is not a tendency 
to bore out deep places in streams above all obstructions, 
partly due to the shock of the water on meeting the ob- 
struction, and partly to the fixing permanently at one 
point, the wave impetus that has been mentioned as 
common to flooded streams, if not in fact to all streams. 

The slope produced in the surface of a stream immediate- 
ly above a fall, due to the ready escape of the water over 
it, would permit the water at the sides to be lifted more 
easily by the outward-moving current at the bottom. This 
would increase the speed of the downward flow through 
the middle, and enable it also to contribute somewhat to 
the scouring out of the bottom. 

Why Floating Material Drifts to the Middle 

OF Streams 

As a result of the double-spiral movement of water in 
streams, and one of the most unanswerable proofs of its 



44 SMITH'S ESSAYS 

existence, may be cited the well-known fact that floating 
material tends to drift from the margins to the middle of 
all enchanneled streams: or as might be better stated, 
that it is the tendency of all streams to carry drift to the 
middle. 

If a stick of wood be placed in the middle of a pond, in a 
few hours it will be found at the edge, where it has 
been drawn by the attraction of the bank: so also when 
rivers are low as in summer and the current is very slug- 
gish, if the banks are high, gravity may cause floatage to 
move to the shore if such floatage be already near to it. 
Winds likewise, may at any time, if sufficiently strong and 
persistent, carry drift to the shore or scatter it over the 
stream. So also, the confusion into which streams are 
frequently thrown when making a sharp bend, will often 
result in a dispersal of the drift, or at least an irregular 
distribution of it. But the tendency is nevertheless, al- 
ways from each side to the current wherever the double- 
spiral obtains, and the forces mentioned merely counter- 
act this tendency for the time being. 

Now no one will contend that the drift that constantly 
moves toward the middle of streams, skips across from the 
margins to the middle and leaves the water behind it. The 
water that bears it up and surrounds it must go with it, 
and the movement of the one is the movement of the other. 

If then it be true that the water of the surface of streams 
everywhere and always is moving from each side toward 
the middle, the conclusion is irresistible, that it must pass 
down through the middle and return to the margins by a 
countercurrent beneath. 

But it is just at this point that the present theory has 



THE LAWS OF RIVER-FLOW 45 

been opposed with the most earnest objections. At the 
meeting of the Mississippi River Commission in St. Louis, 
in 1885, Gen. John Newton, Engineer in Chief of the Unit- 
ed States Army, kindly submitted this theory to the Com- 
mission, with favorable mention, a copy of it having been 
transmitted to him by Gen. W. B. Hazen, Chief of the 
United States Signal Service. 

Objections to the theory were urged by other members 
of the Commission, however, on the ground that pilots 
and river men generally, claimed to have observed that 
floating material is carried away from the middle of streams 
in rising water and scattered over the surface, and that it 
is more difficult to keep tows, rafts and the like, out of the 
banks in rising water than in falling: and that it is only 
when the water is falling that drift gathers at the middle 
of streams. General Newton brought the matter up 
again at a scientific meeting of engineers held later in 
Brooklyn, as the writer was informed by Captain Tuttle, 
Engineer of the Commission, only to meet with the same 
experience as at St. Louis. 

The objection if valid, would be fatal to the theory: and 
it is remarkable with what unanimity it is urged by men 
whose life is on the river. Of quite a considerable number 
of this class of men, to whom the author has broached the 
matter, there have been found very few who,until the self- 
evident fallacy was pointed out to them, did not insist 
that drift scatters from the middle on a rising river. The 
contention is in no sense true, however, of any regulated or 
organized stream, that drift at any time tends to scatter 
from the current. It is based upon an error of observa- 
tion that only needs to be pointed out to stand refuted. 



46 SMITH'S ESSAYS 

To realize the impossibility of the first movement of 
drift being from the middle towards the margin of a stream 
it is only needed to reflect that in low water, there is no 
drift, either at the middle or anywhere else, floating on the 
surface. In low water streams are entirely free from drift. 
Seeing that a river, when low is free from drift, and that 
it must rise before it can fall, how then is it possible for the 
drift to move first from the middle toward the banks. 
Surely it must be carried to the middle before it can be 
carried away from it. 

How has it happened then, that river men almost unani- 
mously agree in this view, and so uniformly fall into this 
self-evident error? As a rule, when a pilot is directing 
his boat on the river, he is looking only for a clear or prac- 
ticable path, and not seeking to ascertain in what direc- 
tion each piece of drift is floating. He fails to take note 
of the fact that the drift is spread over the river, not be- 
cause it is moving away from the middle, but because 
having come in from tributary streams, or having been 
picked up from various points along the bank by the rising 
water, it has not yet had time to reach the middle to which 
it is obliquely moving. 

It must be said, however, in favor of these river men, 
that their mistake is not wholly without some excuse in 
appearances: for drift does probably collect more slowly 
in a very rapidly-rising river, than in a stationary or falling 
one. In the case of a sudden break of a reservoir, or a 
crevasse in a levee, the escaping water would flow away in 
every direction the contour of the land would allow, and 
of course, any drift it might bear would take direction 
with the water. 



THE LAWS OF RI\^R.FLOW 47 

Now in a stream rising very rapidly, similar conditions 
might exist, only in a lesser degree. From the front or 
head of the advancing flood in such cases, there might 
be a slight tendency of the middle to spread out, and a 
little time might be required for the water to rise at the 
banks, and develop sufficiently the potential trough in- 
dispensable to the production of surface inflow. 

And it is not impossible even, that where drift is al- 
ready floating in a stream, and a tributary brings in a 
flood looming up like a great wall of water, this drift 
might be even driven to the shore. But this must happen 
with extreme rarity, and it is still axiomatic that drift 
must go to the middle before it can leave it. 

As to the increased difficulty of keeping river craft out 
of the banks in rising water, that is precisely what the the- 
ory would lead us to expect and is entirely consistent with 
it. 

In a straight stream the two spirals lie side by side,with 
the water from both descending in the middle. But when 
passing a sharp curve along a concave shore, the inner half 
is tilted by its momentum over the outer one, just as the 
inner side of a train of cars tends to tilt over when the train 
is passing around a curve. When this occurs, instead of 
being made up of two spirals lying side by side, the stream 
will then consist of an upper and an under spiral, with the 
surface water of the upper one flowing outward quite to the 
bank. 

And since the current in these cases is at the outer bank, 
carried there with all the greater force by reason of in- 
creased speed in case of floods, a boat pressing toward the 
bank, will be simply drifting with or into the current, in 
accordance with the invariable rule. 



48 SMITH'S ESSAYS 

Direction OF Drift at the Bottom 

At the bottom of streams, on the other hand, as must be 
the case if the theory is true, the movement of sand, pebbles 
and in large rapid streams, of stones of considerable size, 
will be found to be obliquely downward and outward: that 
is to say, diagonally down the stream, from the middle to- 
ward the margins. 

On examining a stream of ordinary dimensions, after a 
flood, it will easily be perceived that the coarser gravel 
occupies the middle of the stream, on the outer side of this 
the finer gravel will be found, next the coarser sand,then 
the finer sand, and finally a deposit consisting wholly of 
mud or clay. 

These deposits will also frequently be found in the form 
of banklets or ridges pointing obliquely from the axis of the 
stream upward and outward toward the banks, thus fur- 
nishing both proof and illustration of the fact that the 
water at the bottom had flowed obliquely downward and 
outward, and had been progressively retarded. Obviously 
only the heaviest gravel could be dropped where the water 
was swiftest, and after that the finer and finer particles 
would be deposited in turn, as the water lost its speed in 
the direction of the margins. 

If we concede that water at and near the surface of 
streams flows obliquely downward and inward toward the 
middle, a fact which can be verified by experiments in the 
reach of every one, we cannot escape the conclusion that 
the principle of the double-spiral governs in stream move- 
ment. Since such inflow is constant, and extends from 
the head of every stream to its mouth, one of three things 



THE LAWS OF RIVER-FLOW 49 

must happen in every instance. Either the water must 
heap up progressively into a ridge in the middle, or in- 
crease in speed of flow, so that at the end of each mile, the 
current will carry a quantity greater by the inflow of one 
mile than it carried the mile above, or the water must sink 
down through the middle and move out at the bottom, to 
return again by the surface. 

But the water in the middle of streams does not heap 
up progressively : it does not increase in speed, for a river 
may flow for thousands of miles without gain in rapidity 
of current : therefore the water must pass down through 
the middle and move in a constant circuit. 

Let us suppose a stream moving with a speed of a mile 
an hour and that continuously every hour, a hundred apples 
should be thrown in at its source, and then that for each 
and every mile of its length for a thousand miles, a hun- 
dred apples should be seen drifting from the edges to the 
middle on either side, and that still only two hundred to 
the mile should be seen drifting towards the middle at 
the mouth of the stream; would we conclude that a hun- 
dred apples to the side had been thrown in every hour for 
every mile of the river's length, or would we conclude 
that the apples thrown in for the first mile had continu- 
ously sunk down through the middle and drifted back 
beneath to the banks, to rise up there and be carried 
again to the middle.^ If the case were otherwise, if 
for either side of the stream a hundred fresh apples to the 
hour were thrown in for every mile of its length, 200,000 
apples to the mile should be found at its mouth and not 
the 200 actually seen. 



50 SMITH'S ESSAYS 

Why the Point of Greatest Speed in Streams is 
Beneath the Surface 

For a long period, doubtless from prehistoric times, it 
has been known that the water in a river or other stream, 
is swifter at points some distance beneath than imme- 
diately at the surface. Men much upon the river must 
have often observed, as they do now, that if a skiff was 
loosed from a larger boat, while both were drifting, the 
boat drifted ahead of the skiff, and if an oar was let fall 
from a skiff, it lagged behind. It was easily and doubt- 
less early perceived, that the cause of this was that the 
boat reached down into a faster moving stratum of water 
than that which carried the skiff, and that the oar which 
floated lightest must be moving in the water that was 
slowest. 

The first known, and for a long time the only explana- 
tion proposed for this phenomenon, was that it is due to 
the friction between the surface of the water and the at- 
mosphere, this being deemed sufficient to account for the 
observed retardation. 

This was the view with which Humphrey and Abbott 
closed their elaborate investigations made in 1846 in con- 
nection with the government survey of the Mississippi. 
They found as the result of numerous measurements, that 
the point of maximum speed for the Mississippi is about 
three-tenths of the depth of the stream beneath the sur- 
face. 

Boileau found the point of maximum velocity, though 
raised a little for calm weather, still a considerable dis- 
tiance below the surface, even when the wind was blowing 



THE LAWS OF RIVER-FLOW 51 

down stream with a velocity greater than that of the 
stream, and when the action of the air must have been an 
accelerating and not a retarding influence. He found also 
as had Humphrey and Abbott, that the depth of the maxi- 
mum speed point varied with the wind. When the wind 
blew up stream the depth was greatest, and it was smallest 
when the wind blew down stream. 

Professor James Thomson, brother of Lord Kelvin, 
has offered an explanation of the diminution of velocity 
at and near the surface of streams, or rather the increased 
speed beneath the surface, which Sir Archibald Geikie, in 
the article on Hydrodynamics in the Encyclopedia Brit- 
annica, pronounces much more plausible than the hypoth- 
esis of friction against the atmosphere. 

Professor Thomson's explanation is, that portions of 
water w^th their velocity diminished from retardation by 
the sides and bottom of the stream-bed, are thrown off in 
eddying masses and mingle with the rest of the stream. 
These eddying masses modify the velocity in all parts of 
the stream, but have the greatest influence at the surface. 
Reaching the free surface they spread out and mingle with 
the water at that level, diminishing the velocity which 
would other w^ise be found there. 

This rising of the water that has been retarded by fric- 
tion against the channel bed, is exactly what the theory of 
the double-spiral requires: but it cannot be accomplished 
in the way that Professor Thomson suggests. 

In the first place, though it is true, as we have already 
seen, that retarded particles of water gather into larger 
masses, and these on being collided wath by other and 
faster-moving masses, are driven or projected upward 



52 SMITH'S ESSAYS 

for the most part by way of the sloping banks. These 
masses do not reach the surface as a rule, except near the 
margins, where the movement of the whole of that part of 
the stream is upward. 

In the second place, if the masses of retarded water 
should rise to the surface after or because their motion 
had been retarded, it would be necessary for them to make 
their way through the more rapidly-moving central por- 
tions of the stream, and they would thereby necessarily 
acquire a similar speed. Other objections still might be 
urged to this hypothesis. 

This suggestion of Professor Thomson is, however, an 
important one, coming as it does from an acute observer 
and profound thinker, and pointing out the only possible 
source of the retardation we are here considering. It only 
needs to supplement it with the recognition of a syste- 
matic method, by which the retarded masses, regularly 
and continuously, reach and spread out over the surface. 
On the principle of the double-spiral, the explanation be- 
comes simple, clear and easy. 

The strata of water in contact with the channel wall are 
retarded by friction, as they steadily make their way along 
the bottom in the direction of the margins of the stream, 
this retardation being communicated from stratum, to 
stratum and diminishing from below upwards to the point 
of maximum speed. It, of course, reaches its greatest 
extent at the margin of the stream, and the water rising 
there, spreads out over, or rather shears over toward the 
middle as the upper half of the stream. 

It needs to be remembered, that the water moves out 
beneath, by reason of the fact that a way is cleared for it 



THE LAWS OF EI\TR-FLOW 53 

by the progressive retardation, that is to say, it is par+ly 
pulled along, as it were, or drawn into an infinite number 
of quasi vacuoles. By this outvv^ard movement the water 
is partly drawn down in the middle. It is not to be sup- 
posed, however, that the wp^ter of each of the spirals folds 
over as if consisting of so many laminae-like sheets of 
paper, that strictly keep their places. All along the edges 
of streams, and in fact all over the bottom, there will be 
irregular breaks: and where the bottom is rough these 
breaks may be quite extensive. When this is the case the 
water will fly off in innumerable masses of various dimen- 
sions, mainly in an upward direction, and near the edges 
as already stated, these masses will manifest themselves 
by boiling up through the free surface. 

It is not necessary, however, for these masses to pass 
quite through the body of the stream in order to show at 
the surface, for the impulse at the bottom may be passed 
from mass to mass until it causes the waiter to boil up 
through the surface even in the middle of the stream, al- 
though each mass in its turn may have moved but a short 
distance in the direction of the surface. 

A beautiful illustration of this arrangement may at any 
time be witnessed, by looking down onto the surface of a 
river swollen into a stage of flood. The water here for 
perhaps a fourth of the stream width on either side 
but not immediately at the bank, will be seen boiling up 
in irregular s^^rls throughout its whole extent. Within 
and next to these strips or borders, will be seen two 
smooth bands like broad metallic ribbons. Between 
these again, the current rushes, a narrow strip rough with 
wavelets or ripples. 



54 SMITH'S ESSAYS 

This roughness of the surface along the line of the cur- 
rent, is probably due to slack rather than to greater speed : 
the water is moving in from the sides faster than it can 
sink down in the middle. That the roughness of the sur- 
face of the current cannot be due to speed alone, is clearly 
indicated by the fact that the smooth band on either side 
in the larger streams may be moving much faster than the 
rough surface-current of other and smaller streams. 

The position of the locus of greatest speed as well as its 
origin, is also susceptible of explanation on the theory of 
the double-spiral. Ordinarily the swiftest part of a 
stream, as already stated, is at a point three-tenths of the 
distance from the surface toward the bottom. This 
would allow one-half of the stream to be moving inward 
above, and the other half outward beneath the horizontal 
plane of the swiftest part. For while the upper part is the 
wider and the swifter, the lower half though slower, is the 
deeper. 

When the wind blows up stream, the swiftest point 
goes deeper, for the reason that in such case the upper part 
being made to move more slowly, it must have a larger 
volume in order to constitute half of the movement. On 
the other hand, when the wind blows down stream, the 
upper half becomes more swift, and does not need a depth 
of three-tenths in order to embrace half of the movement, 
and the maximum speed point consequently rises. The 
controlling condition obviously is, that the same quantity 
of water must move out below the plane of greatest speed, 
that moves inward above it. 

Reflection will also make manifest, that the half of the 
stream that is moving inward above, and the half that is 



THE LAWS OF RIVER-FLOW 55 

moving outward below, must have imiform speed at their 
points of contact. The speed of the upper half is continu- 
ously accelerated as it moves in toward the stream axis, 
and that of the lower half is in like manner retarded as it 
moves out, and thus the highest speed of each division is 
found in their plane of contact. 

The speed of the upper half will, it is true, increase more 
rapidly than the retardation of the lower half, but since 
the water of the upper half has a more rapid motion in the 
line of the stream axis, the transverse, or in and out move- 
ment of the two parts, will be equal at corresponding 
points. 

Why Streams are Highest in the Middle 

The surface of streams has been previously character- 
ized as trouc^h-shaped )r concave on transverse measure- 
ment, and this is given as the cause of the inward flow of 
the upper porti )n. Yet as a matter of fact, the stream 
surface probably never presents this form, unless it be 
just below dams or cataracts, or on the slope of surfaces 
bordering on the sea as the tide goes out. On the con- 
trary, w4th possibly the exception named, the middle is 
probably always as high as the margins, and in rapid 
streams invariably higher. At the Yukon Rapids the 
surface of the river at the middle is said to be six feet 
higher than at the margins. 

This peculiarity of the elevation of the middle of streams 
has been for a long time observed, and two theories have 
been offered in explanation )f it : one by Maj jr Allan Cun- 
ningham, R. E. of the British army in India, and the 



56 SMITH'S ESSAYS 

other by no less distinguished a personage than Sir Isaac 
Newton. 

The explanation offered by Major Cunningham is that 
pressure in water is diminished by speed, and as the speed 
of those parts of a stream forming the current is the greater 
the water in the line of the current becomes elevated. 

The explanation long before offered by Sir Isaac New- 
ton, is not materially different. In fact when carefully 
analyzed, the theory of Major Cunningham is but a re- 
statement, in different language, of that of Sir Isaac New- 
ton. It was held by Newton, that friction at the margin 
of streams pulls down the water, while the middle being 
less subject to friction, remains elevated in the form of a 
ridge. To this view there are many objections. 

In the first place, no such momentum could pertain to 
water in any stream, as would be required to hold the 
middle up in this way to any appreciable extent. Let us 
suppose for illustration, that a stream with a fall of ten 
feet to the mile, has a speed of ten miles to the hour, and 
at the end of one hour, has the middle elevated one foot as 
it was at the start, this initial elevation being due to 
a like incline of the stream farther up in its course. 

This signifies that the water forming the ridge would not 
fall from the line of a straight projectory, in the smallest 
degree, in a period of one hour. Or if we suppose the water 
of the stream at the start to have had a level projectory, 
the middle would have fallen below it by only one hundred 
feet in one hour. Now the most powerful cannon in ex- 
istence cannot send a ball with a projectory so nearly 
level for ten or even five seconds. 



THE LAWS OF RIVER-FLOW 57 

But at the end of the hour the margins of the stream are 
only one foot lower than the middle, just as at the start. 
It would appear then, that the middle is as much pulled 
down by the friction as the margins, and the margins as 
much held up by momentum as the middle. 

Again: continuing the assumption that the elevated 
ridge in the middle of streams is due to momentum, sup- 
pose that a stream after falling over a dam and losing its 
ridge, moves with such speed that it regains the ridge ex- 
actly at the end of a mile, and that this ridge has a height 
of six inches. At the end of two miles, the ridge ought to 
be twelve inches high, at four it should be two feet, and so 
on until the stream should stand on its edge like a board. 

Still another difficulty is found in the logical deduction, 
that if friction at the banks pulls down the margins of a 
stream, the friction of the channel walls at the middle 
ought to pull down the bottom of the stream. But since 
the top according to the explanation under consideration 
must remain in the air by reason of its momentum, this 
in all rapid streams, should result in pulling the top and 
the bottom apart, thus making them hollow at the center. 

The simple explanation offered by the theory of the 
double-spiral is, that when the water that constitutes the 
sides or borders of the trough into which every stream is 
resolved by the momentum of the outward undercurrent, 
reaches the elevated edges it begins to flow back toward 
the lowered middle of the stream. But at every point, on 
transverse section, this depressed middle or trough, is 
found already filled up by water flowing in from the mar- 
gins immediately higher up. Each portion of the water 
of the marginal elevation, must, therefore, move obliquely 



58 SMITHES ESSAYS 

down the stream until it reaches a point in the surface of 
the middle lower than that from which it started. 

The tendency of the action of gravity would of course 
be to reduce the surface to a level, or preserve it in the form 
of a level, but the momentum gained by the water flowing 
in, is suflBcient partly to overcome the influence of gravity, 
and the flow from the two sides will consequently raise 
the middle of the stream into a ridge. Thus every stream 
of water moving in an open channel, presents the paradox 
of a surface that is at the same time concave and convex, a 
trough and a ridge : that is potentially a trough but actually 
a ridge. Ordinarily only the ridge is in evidence, but if 
across the surface of a stream we measure a curve with the 
convexity downward in the direction of the flow, we will 
invariably find an actual trough. 

But while the middle at any point in the continuity of a 
stream may almost invariably be found on transverse 
measurement, to be higher than the edges, the particles 
of which the raised middle consists, will not in any case 
have reached their position from a lower level. On the con- 
trary, every particle of the water will be found at a lower 
level than when it left the bank: no particle forming the 
middle has flowed up hill. 

Why Delta Streams Throw up Levees along 

Their Banks 

All rivers reaching the sea through deltas formed of 
their own deposit of silt, have their banks elevated above 
the general level of the land back of them, so that such 
streams as a rule, flow in channels apparently scooped out 



THE LAWS OF RIVER-FLOW 



59 



of the crest of a low ridge. Inspection of the cross section 
of the bed of a delta river, will reveal that the highest 
part of the land is that immediately next to the river. 
From this point on both sides, the land has a gradual 
downward slope, usually terminating in a nearly level 
plain consisting of swamp or marsh. 

The only arable lands along the lower portions of the 
course of many rivers consists of the elevations formed of 
silt which has been cast out upon the banks, either by the 
main stream, or by one of the numerous outlets they have 
constructed from time to time as they pushed their way 
farther and farther into the sea. 

During floods the transverse currents at the bottom of 
rivers cast the silt out over the banks on both sides, where 
on account of the slowdng of the flow, it is precipitated and 
deposited. As a consequence of the most rapid movement 
of the water being nearest the banks, that part of the de- 
posit closest to the stream always consists of the coarsest 
particles that enter into the composition of the silt. Out- 
side of this coarse material, finer silt is deposited, and still 
further out, where the water has almost lost its motion, 
the very finest particles are deposited. These are often 
so fine indeed, that they are easily spread out over large 
areas, resulting in the formation of wide stretches of land 
almost as level as the sea. This will readily appear from 
the illustration. 




Fig. 9t: 

SECTION OF DELTA BIVER BED. 



60 SMITH'S ESSAYS 

Year by year and century by century, the river gains in 
length by the deposit of silt in the sea, near its mouth, and 
with each increase in length a higher bed is required for its 
channel. With a higher bed for the channel of the stream 
higher walls are required all along its course for the re- 
straint of overflow, and these walls grow up by the deposit 
of uplifted and ejected silt. 

Where for long periods, rivers have been prevented by 
artificial embankments from overflowing the adjacent ter- 
ritory and raising its level by the deposit of silt, it hp^s 
sometimes happened that the streambeds have been 
raised entirely above the general level of the land. 

Why Delta Rivers Have Multiple Mouths 

Rivers that have formed deltas at their outlet into the 
sea, very uniformly have multiple mouths. The number 
of these outlets may sometimes run into the hundreds, 
and they too are a product of the double-spiral. 

In order that erosion may be effected in channels, as al- 
ready explained, a certain relation is required to be main- 
tained between the width and the depth. When the width 
is too great in proportion to the depth, the water breaks 
up into a number of spirals, each pair of them proceed- 
ing to cut a new channel. Thus if a mill-dam be thrown 
across the channel of a very crooked stream, it will result 
that when the stream overflows, as during freshets, it will 
be caused to spread over the land to such an extent that a 
number of spirals must be formed, and in this way the 
projecting point of land at each sharp curve will be cut off 
in time, and be left as a small island in the mill-pond. 



THE LAWS OF RnT:R-FLOW 61 

So when a silt-bearing river reaches the sea, the speed 
of its water is arrested as it spreads out over the heavier 
salt water and a deposit of silt takes place and this forms 
a bar at the point of entrance. 

The double-spiral in order to effect erosion, as already 
explained, requires that there shall be a certain proportion 
between the width and the depth of the flow. A stream 
that might maintain a single double-spiral across its bar, 
in high water, would in low water break up into a number 
of double-spirals for when the water should spread out 
from the axial line the friction would be too great to 
permit it to return. 

Each pair of these spirals would then proceed to cut a 
channel across the bar, which might in time become an out- 
let. Succeeding floods would fail to obliterate entirely 
the whole of the notches thus cut into the bar, and such 
as thus escaped, would be cut deeper during each suc- 
cessive season of low water, and lengthened out into the 
sea by each successive flood. 

As the incline of the channel of each of these outlets 
must be extremely small, since this channel formation be- 
gins at sea level, the current will be necessarily slow and it 
will become slower in proportion as the length of such out- 
let becomes greater. In the course of time, the current 
in such of these cutlets as are given off at points f farthest 
from the sea, becomes too slow to carry away the silt that 
is thrown into their channels at their sources, by the 
transverse undercurrent of the parent stream. In such 
cases the inlets or heads of these channels are filled up with 
silt, and thus shut off from the main channel. 

In the meantime, as the sea is caused to recede by reason 



62 SMITH'S ESSAYS 

of the deposit of silt, the main stream will be less inter- 
fered with in its spiral action. By the elevation of its bed 
it will be still farther removed from the interference of the 
sea : so that in the course of time it will select that one of 
its outlets which proves to be the line of least resistance, 
and widening and deepening it into dimensions suitable for 
the main channel, it will close up the other more slug- 
gish outlets, and push its way as one body farther out 
toward the sea. The longer outlets, filled up in this way 
at their source, become the "blind bayous" so frequently 
met with in all considerable deltas. 

Kinetic Equilibrium in Streams 

While a solid body is falling through space it increases 
in speed indefinitely, and the distance it will fall in any 
given time is the distance it will fall in one second, multi- 
plied by the square of the number of seconds it is falling. 
If it be allowed to slide down an inclined plane, there is a 
lessening in the rate proportional to the resistance it meets 
since the force expended in friction in its oblique move- 
ment, must be subtracted from that developed in the fall 
of a body through free space; but the ratio of fall per sec- 
ond — per second — the ratio of acceleration is the same. 

With liquids flowing in a channel the case is different: 
for in a very short time, water flowing down an inclined 
channel, reaches its highest attainable speed under such 
conditions that is it attains what is known as kinetic equi- 
librium. And curiously enough, it is not in the steepest 
channels that water flows fastest. 

A distinguished French scientist, M. Vallot, (Nature, 



THE LAWS OF RIVER-FLOW 63 

Vol. 65 P 32.) records a series of experiments mj^de by 
himself, in which it was demonstrated that when the in- 
cline of the channel is more than three feet to the hundred, 
the speed of the water actually diminishes. The greatest 
speed according to M. Vallot, was given in a channel of 
three feet of incline to the himdred : the speed diminishing 
in channels with a coefficient of incline either below or 
above that figure. It is more than likely that this is not 
the fixed rule for all sizes of channels, for in large streams 
the amount of friction against the channel walls is much 
less proportionally, than in small ones. But the discovery 
is a curious and interesting one in connection with streams 
of whatever dimension. 

WTien Napoleon, with a view to avoiding interference 
at the hands of the British, undertook the construction of 
ships in Lake Constance, his engineers constructed a flume 
of hewn logs framed together, in which to slide the timbers 
from the heights of Mount Pilatus into the lake, a dis- 
tance of something like six miles. 

At first an attempt was made to slide the timbers down 
the dry flume. So great, however, was the speed acquired 
by the timbers in their descent, that such heat was devel- 
oped as threatened speedily to destroy the flume, while the 
timbers themselves were materially damaged by it. 

It w^as thereupon decided to direct into the flume a small 
stream of water, which was found near its head. When, 
after this w^as done, the logs were let slide, they moved 
down with speed increasing to the end, and so great was 
the momentum acquired, that when they reached the lake 
they plunged through some thirty feet of water with suffi- 
cient force often, to stick into the mud at the bottom. 



64 SMITH'S ESSAYS 

On the other hand, the stream of water increased in speed 
for only a few rods, and thereafter continued on to the lake 
without further acceleration. 

For this peculiarity of movement which pertains to all 
enchanneled streams, no satisfactory explanation, insofar 
as the writer is advised, has ever been proposed. On the 
principle of the double-spiral, it admits of simple and ready 
explanation. 

Since the oblique currents in a stream depend altogether 
upon friction against the walls of its channel, the acute- 
ness of their angle of flow with reference to the stream 
axis, will increase in proportion to the increasing shallow- 
ness of the water and its speed: that is, the pitch of the 
helix rises as the speed of the stream increases. 

In a dcx^.p, slow-moving stream the spiral flow will have 
a very small incline t > the axis a,nd the helix will be lew, 
but in a swift, shallow stream the spiral flow will be more 
nearly transverse, and with a more obtuse angle to the 
stream axis. The mountain stream dissipates the energy 
it develops in its fall, simply in beating transversely against 
the walls of its channel and in the impact of the incoming 
parts of the transverse currents against each other as they 
meet in the middle. 

It is true that large streams flowing partly through low 
plains almost at sea level, and partly in mountain channels 
of great incline, have a speed well-nigh as grea.t in the 
plains as in the mountain stretches, and this at first blush 
would seem to oppose the foregoing contention. The 
reason that the transverse movement is not so great in the 
plains as in the mountains, though the progressive move- 
ment of the water is practically the same, is that boulders 



THE LAWS OF RIVEE-FLOW 65 

and coarse detritus gathered in the mountains, are ground 
into fine silt as they reach the plains. This faciHtates 
the deeper erosion of channels in the plains, and reduces 
friction and consequent transverse motion, both by afford- 
ing a smoother bed and a greater depth of water. 

The Value of Curves 

In this connection we may also refer to another feature 
of rivers, not wholly unconnected with the one under con- 
sideration, and that is the relative economy of energy 
expenditure in streams when moving in a straight channel, 
and in those moving in curved and sinuous channels. 

There can be little question that the typical channel is 
trapezoidal or broadly trough-shaped and perfectly 
straight. In such a channel, if made in hard material, 
with friction reduced to the minimum, doubtless there 
would be attained the greatest speed and the greatest dis- 
charge possible. But in streams as they are found exist- 
ing in nature, these conditions are never fully attained. 
The accumulation of sand and gravel, together with irregu- 
lar erosion, invariably cause irregular distribution of 
friction and retardation. 

It is to escape this irregular and excessive friction, that 
rivers oscillate from side to side with or in their channels, 
like a team of oxen drawing a heavy load, or a camel 
swaying along a desert path. 

When the stream is making a curve and the swiftest 
parts of the two spirals are throT^oi to the concave bank, 
there Is produced the greatest erosive effect possible to it. 
We found that in pools which in low water are practically 



66 SMITH'S ESSAYS 

without current, a greater erosive power exists than in 
shallows when during freshets an equal addition is made to 
the depth of both. In bends the speed near the concave 
bank is usually exceptionally great because the deepest 
and most rapid parts of both spirals are thrown to the 
bank: and since the inner spiral is superimposed on the 
outer, the friction surface is there reduced to a minimum. 
On the other hand, the broad shallow part of the river 
or other stream toward the convex bank has relatively so 
large and area of bottom on which to develop friction 
that the transverse undercurrent has an exceptionally 
large angle to the stream axis. On account of the rela- 
tively great extent of friction the movement of the water 
is correspondingly slow in this part of the stream. 

The energy developed by the fall in sinuous streams is 
mostly restricted to the convex side: and it is a question 
whether nature ever presents a stream in which a sinuous 
channel does not on the whole give some advantage in the 
way of speed; that is to say, it may be that water will 
traverse the entire length of a river in less time when its 
course is somewhat winding with alternate deeps and shal- 
lows than when it is straight but uniformly shallow. 

There can at all events be no question, that for a short 
distance cr for a single stretch, the channel-making power 
is greater in a curved stream than in a straight one. It 
has been noted that the deepening of chi^.nnels at the 
mouths of rivers, is promoted by the curving of the stream 
toward the side opposite that to which the rotation of the 
earth tends to direct it. That is, if the earth's rotation 
causes the river to carry its deposit to the right, the out- 
let channel that bends around this deposit with its con- 
vexity to the left, will be deepest. 



THE LAWS OF RIVER-FLOW 67 

This is further and well shown by the results of attenxpts 
at channel deepening for harbors. The very few under- 
takings of this kind that have been successful, have been 
worked out with curved channels, and mostly with chan- 
nels having the natural bank for one wall, and a single 
line of jetties on the other to throw the water against this 
bank. 

Regulation and Regimen of Channels 

It is the law governing the relation of width to depth, 
as exhibited in the formula already pointed out, that de- 
termines for each particular stream, the size of its chan- 
nel. Streams flowing from springs where the quantity of 
water is fairly constant, always carve out channels of ap- 
propriate dimensions, and never overflow their banks, and 
the same may be said of all streams kept up by a steady 
supply of water. If the Amazon at its highest flood, could 
be turned into the Mississippi and maintained with an 
even volume, in the course of no great lapse of time it 
would carve out or build up for itself a suitable channel 
and remain within its banks. All rivers would regulate 
their channels in the course of time and remain within 
their banks, even in seasons of flood, except for the contin- 
uous lengthening they experience at their mouths, and the 
excess of coarse detritus that is carried into their channels 
from elevated slopes. 

So long as additions to the length of rivers are made by 
deposits of silt at their mouths, the banks along their en- 
tire course from the outlet up to the first considerable 
fall, must as already pointed out, be constantly raised to 



68 SMITH'S ESSAYS 

greater and greater heights in order to prevent overflow. 
Likewise if detritus, such as coarse sand and gravel, be 
carried into streams just as rapidly as it can be ground up 
and suspended in the water, the deepening of the channel 
will be arrested: when the accession of detritus exceeds 
this rate, the channel begins to fill. Related to this is an 
interesting feature of the behavior of youthful rivers, that 
has sometimes proved a puzzle to geologists, and to which 
in the present condition of rivers there is oflFered no parallel. 
As the earth slowly rose from the sea during early geologic 
uplifts, presenting vast level stretches of land, the rivers 
born of the enormous rainfall of those early ages, spread 
out widely, and in consequence detritus was deposited 
in vast strata, in marked contrast with the restricted de- 
posit possible to present matured rivers. 

Bodies of the Drowned Drift to the Shore 

The situation in which the bodies of those who have 
been drowned in rivers are usually found, also bears evi- 
dence to an outward movement of the water at the bottom 
of streams. Such bodies, no matter in what part of the 
stream the drowning may have occurred, are foimd when 
they rise of themselves, almost invariably at the banks. 
If the fact of an outward underflow is conceded, this ad- 
mits of a ready explanation. 

When a person is drowned, the body being of a slightly 
greater specific weight than water, sinks to the bottom. 
After an uncertain or varying period, internal decomposi- 
tion sets in, and the body is rendered specifically lighter 
by the accumulation of gases generated thereby. When 



THE LAWS OF RIVER-FLOW 69 

it attains the exact specific weight of the water, it begins 
to drift. Usually it maintains this specific weight long 
enough to reach the shore on one side or the other, and 
there it adheres until it is discovered. 

Rising of Streams Below Waterfalls 

The orderly and organized movement of water in chan- 
nels, which is secured and controlled by the double-spiral, 
vastly affects the amount which a given width and depth 
of stream can deliver. A much greater area of cross sec- 
tion is required to convey a given quantity of water in a 
confused, disorderly stream, than in one that is orderly 
and organized. A marked illustration of this is presented 
in the more rapid rise of streams below than above dams 
and such like obstructions during floods. In these cases 
the breaking up of the double-spiral confuses and thus 
impedes the water in its flow. 

As an example of the effect of this character of dis- 
turbance, may be cited the case of the falls of the Ohio 
at Louisville. At the lowest stage of water in this river, 
the fall of the surface from First to Fifteenth street, a dis- 
tance of about a mile and a quarter, is 27 feet. At a 2.5 
foot stage, the fall is 26 feet : at a 7.5 foot stage it is 21 feet : 
at a 46 foot stage it is 1.6 feet, within the limits given. 
Owang to the breaking up of the double-spiral, the fall in 
this as in all similar cases, is during floods stretched over a 
long section of river. 

It is true the great facility of discharge over the falls, the 
Ohio being exceptionally broad at this point, and also the 
marked narrowing of the channel below the falls, has not 



70 SMITH'S ESSAYS 

a little to do with the result in this case. But observa- 
tion will develop that the rule holds good with all dams and 
all natural waterfalls. 

In the year 1883 at Davis's Bend in Louisiana, some 
twenty miles above New Orleans, there occurred a crevasse 
in the levee, permitting about one-third of the water of the 
Mississippi to escape, this water flowing directly across 
the swamps into the Gulf of Mexico. 

The distance from the Mississippi to sea level in this 
part of its course is about twenty miles, and the total in- 
cline of the surface of the land is about nine feet or nearly 
six inches to the mile. And yet such was the hindrance 
to the flow of the escaping water, due to the want of a 
rightly-proportioned channel with its resulting organized 
double-spiral movement, that the water spread out over a 
territory extending up and down the river for a distance 
of 80 miles. In some places this flood water was more than 
twelve feet deep and almost as still as a lake. So slug- 
gishly did it move, that some of the New Orleans papers 
suggested that the grass of the swamps, and the water 
plants, must have dammed up the water and restrained 
its flow. 

And yet at the same time the Mississippi, with its or- 
derly current and in its accustomed channel, was carrying 
the remaining two-thirds of the water to the Gulf of 
Mexico, a distance of 127 miles, at a rate of speed of from 
five to seven miles an hour: and this in a channel remark- 
able for its crookedness, and with a normal fall of a little 
more than one inch to the mile. 



THE LAWS OF RIVER-FLOW 71 

The Assembling of Streams 

The characteristic of streams by which those favorably 
situated invade the watersheds of other streams, and di- 
vert their flow, depends also upon the double-spiral, since 
without its aid channels could neither be formed nor en- 
larged. If a perfect plane of considerable extent should 
be provided of sufficient incline for drainage, even though 
without constructional depressions, in course of time all 
its streams having any great distance to flow would gather 
into a few large rivers. 

A stream here and there from some accidental advan- 
tage, would outgrow its neighbors and encroach upon their 
watersheds, and thus force them to join it. Its advan- 
tage would increase with each accession, both in channel 
formation and in the shaping of drainage area, until finally 
a few large rivers, or may be even one, would drain the 
entire region. 

Even underground streams get together in the same 
way, and in some instances, such streams combine to form 
veritable subterranean rivers. 

Deductive Proof of the Double-Spiral 

To the foregoing presentation of arguments based on 
induction, some further support may be supplied from 
reasoning based on deductive principles. With this view, 
let us conceive a stream to consist of perpendicular col- 
umns of molecules as in the illustration, (Fig. 3) and 
that a row of these columns extending longitudinally and 
parallel with the stream axis, is taken for observation. 



72 



SMITH'S ESSAYS 



<l 




o 


/ 


Jf 




a 


U Ir C CO 



Fig. 3. 



Obviously since the lower end of each of these columns 
is known to be retarded, and also more retarded than the 
upper extremity, it follows that in time they will all come 
to lean downward in the direction of the flow of the stream. 
When thus leaning, they will not be able to reach the sur- 
face at the level which the stream must necessarily main- 
tain in order to enable it to conserve its area, and to 
carry the quantity of water it is required to convey. 

At a, for instance, the top of one of these columns will 
reach the surface at 1 : at b it can rise no higher than 2, at 
c, it will be down to 3, and by the time the column arrives 
at d, it will, like all the rest in turn, lie flat on the bottom. 
Thus unless by means of some mechanism not as yet ad- 
mittedly operative, the columns Ccin receive additions to 
their length, enabling them to reach the surface at the re- 
quired level, the stream must eventually fail and disappear 
from very shallowness. 

On the other hand, let us conceive the stream to be con- 
stituted of perpendicular columns of molecules as before, 



THE LAWS OF RI\^R-FLOW 



73 



and a row of such columns on cross section, to be taken for 
observation. (Fig. 4) 




Fig. 4. 



In this case, as the stream moves on, the column of 
molecules next the bank on either side, will be retarded and 
that too progressively and continuously. The result of 
this will be that the entire stream must in time come to a 
complete standstill. For after the motion of the outer- 
most column has been arrested, the next within must ex- 
perience the same quantity and character of friction that 
arrested the first, and it too must come to complete rest. 
This must progress until all the columns have been ar- 
rested in like manner, and then the stream will have failed 
from very narrowness. If, however, a mechanism be 
provided for lengthening out the columns in the first 
example, or for substituting more swiftly-moving col- 
umns for the retarded ones in the second example, the 
stream may continue on without diminution of volume. 

The Lesson of Experiments 



It has happened many times, when this theory has been 



n SMITHES ESSAYS 

submitted to men from whom on account of their position 
and opportunities, one might have hoped to receive a help- 
ful judgment, that the reply even when so respectful 
a level was reached, has been 'Trove your theory by 
experiments." 

And yet when one considers how many volumes of ex- 
periments have been published by competent men, work- 
ing under the most favorable conditions, and what an in- 
finitely greater number of experiments have been made 
and never published, and all without claim by a single in- 
vestigator, of having made even an approach to the full 
solution of the problem, it reconciles one to the almost 
contemptuous replies one often gets from men eminently 
favored by position and opportunity, for forming an in- 
telligent opinion on the subject. 

It may, indeed, well appear to such as consider them- 
selves by reason of the accident of office, lords by pre- 
scription of the fields of engineering science, to be some- 
thing akin to "les majeste" for mere amateurs and on- 
lookers, to venture to work over their abandoned mines, 
and claim to have brought from them the vainly sought 
treasure. Yet with due respect to all such favored guar- 
dians of the sacred precincts of learning, it is confidently 
maintained that the results justify the claim. 

But before offering the results of his own experiments, 
the author may be permitted to pave the way, by citing 
the reported observations and experiments separately 
made by two of the most eminent and capable men who 
have given the matter consideration, namely: Professor 
James Thomson, brother of Lord Kelvin, already re- 
ferred to, and Major Allan Cunningham of the Royal 



THE LAWS OF RIVER-FLOW U 

Engineers in India. For, after putting together the re- 
sults reached by these two eminent investigators, there will 
be little need of dependence on his own. 

Experiments of Prof. James Thomson 

In the minutes of the transactions of the British Asso- 
ciation for the Advancement of Science, for the meeting 
held in Glasgow in 1876, we find the following recorded on 
page 31, being a continued report of Professor Thomson 
on fluids. 

'*The chief view," says the report, *'now experiment- 
ally proved, was that the water in turning the bend exerts 
centrifugal force, but that a thin lamina of the water at 
the bottom or in close proximity to the bed of the river, is 
retarded by friction at the river bed, and so exerts less cen- 
trifugal force than do like portions of the great body of 
water flowing over it in less close proximity to the river 
bed. Consequently the bottom layer flows inwardly to- 
ward the inner bank, and rises up in a retarded condition 
between the inner bank and the rapidly-flowing water, 
and protects the inner bank from the scour, and brings 
with it sand and other detritus from the bottom, which it 
deposits along the river bank. The apparatus showed 
a small river about 8 inches wide and an inch deep, flowing 
around a bend and exhibiting very completely the phe- 
nomena which had been anticipated." 

Experiments of Major Cunningham 

In a review by the editor of ''Nature," (Vol. xxv, page 
1) of a two-volume report by Major Allan Cunningham, 



76 SMITH'S ESSAYS 

giving the result of many thousand experiments made by 
him in India, occurs this language: "His own float obser- 
servations show that near the edges of the stream there is 
a persistent flow of water at and near the surface, from 
the edge toward the center," and again, "The motion of 
the water at each point varies in magnitude and direc- 
tion from instant to instant." 

The outward movement at the bottom, or concave side, 
of the bend in a stream, as demonstrated by Professor 
Thomson, is very readily demonstrated by experiment, 
and is exceptionally easy to observe in nature. As stated 
by him, the centrifugal force on the outside of bends car- 
ries the current to the concave bank. The transverse 
undercurrent in such cases, moving out to the convex bank, 
is made to travel nearly twice as far as it must do in a 
stream taking a straight course: consequently both its 
transverse direction and its retardation become marked 
and distinct, and also easy to demonstrate. 

But such an outward undercurrent, we may be sure, 
existed on both sides of the stream before this bend was 
reached, only in a slighter degree. We may justly as- 
sume then that the experiments of Professor Thomson 
have established the fact of a constant oblique outflow of 
the water at the bottom of streams. 

Major Cunningham, as we have seen, drawing his con- 
clusions from more than forty thousand experiments made 
on the Ganges canal in India, under government auspices, 
and reported in his official capacity, declares that near the 
edge of streams there is a persistent flow of water at and 
near the surface, from the edges toward the center. 

Now if we reflect that owing to the greater speed of the 



THE LAWS OF RIVER-FLOW 77 

water as it nears the center, its longitudinal or axial mo- 
tion greatly increases relatively to its transverse motion, 
we can easily see how it might have been that Major Cun- 
ningham, in his experiments overlooked the transverse 
movement nearer the center. Thus supplemented, we 
have Professor Thomson's experiments establishing the 
fact of the outward undercurrent, and the oiSScial report 
of Major Cunningham affirming the flow from both sides 
at and near the surface toward the center. With inward 
flow at the top conceded and outward flow at the bottom 
demonstrated, the doTVTiward flow in the middle and the 
upward flow at the edges necessarily follow. 

My own experiments do little more than simply bear 
out the others mentioned. As for the inward flow of water 
at the surface of streams, by throwing light substances 
into natural streams mainly, but often into artificial 
canals, the author has observed this times without num- 
ber, in experiments repeated through more than thirty 
years. The outward flow at the bottom is not so easy to 
demonstrate experim-entally. That tendency of the mo- 
tion of the water at each point to vary in magnitude and 
direction from instant to instant, as described by Major 
Cunningham, is only too much in evidence. 

In such artificial canals as are ordinarily used for ex- 
periment, the author has not been able to obtain altogether 
satisfactory results from causing free materials to be car- 
ried along by the water. The general trend of the motion 
of the water may, however, be satisfactorily ascertained 
by attaching substances of near the specific weight of 
water to long strands of thread, and then holding these so 
that the testing floats of about the specific weight of water, 



n SMITH'S ESSAYS 

may occupy the middle or the sides of the stream, as may 
be desired. The total result of numerous experiments of 
this kind, has been such as to confirm the conclusions 
drawn from so many other sources. 

Vital Importance of the Principle 

In bringing to a conclusion the evidence in support of 
the contention that the double-spiral is the essential factor 
in channel formation and stream control, it remains to al- 
lude briefly to the importance that the principle through 
its results, possesses for the human race, an importance 
measured by the value of channeled streams themselves, 
since without the operation of this principle such streams 
could never have come into being. 

It is quite evident, indeed, if the principlehere contended 
for is true — ^if the true theory of streams has here been 
disclosed — no channel formation could ever have taken 
place except in the way described, and the earth had been 
left without a brook or a river. 

In that event, the lowlands of the earth must have pre- 
sented only a dreary expanse of seething, poisonous swamp 
and marsh, wherever seasonable rains might have fallen, 
and the surface of the land had everywhere remained 
almost as it arose from the sea. 

The fact that water becomes lighter as it freezes, and 
that winter covers the rivers with ice, instead of filling 
them up and obliterating their channels, has been consid- 
ered a matter so vital in its bearing on the welfare of the 
denizens of the earth, and especially on the well-being of 
mankind, that it has been widely adduced as an evidence 



THE LAWS OF RI\1ER-FL0W 79 

of special providential care on the part of the Creator. 
Yet even without this provision, we should still have had 
left to us, undisturbed by winter's cold, and unaffected 
by sinking ice, all the rivers of the tropics and of the adja- 
cent parts of the temperate zones. 

But in the absence of the principle here contended for, 
the maintenance of human life on the earth had scarcely 
been possible, and its development to anything like its 
present exalted standard absolutely so. Only in a few 
elevated situations could any dwelling place for human 
beings have been found, and that of the most inhospit- 
able character. There could have been brought into ex- 
istence, nothing of the pleasing alternation of hill and val- 
ley, of swell and swale, of rolling plain and fluted mountain 
slope, that in endless variety, have so lavishly endowed 
the earth with its boundless wealth of charm and beauty. 

First the table lands had to be notched by the channels 
of streams whose very existence was rendered possible, only 
by the concentrated flow of water : and then the ceaseless 
chiseling of wind and rain, of heat and cold, shaped the 
rugged banks into graceful slopes, and embellished the 
mountain sides with a marvelous wealth of sculptured 
architecture. 

Even the utility and attractiveness of the ocean are im- 
measurably enhanced by this power of channel-forming 
possessed by flowing water. For the harbors whose pro- 
tecting arm and inviting quiet, have led the great cities to 
gather and cluster about their shores in order to share the 
generous tribute of commerce and travel, have nearly all 
been brought into being by the subsidence of areas of land 
into which valleys and canyons had been carved by creek§ 
and rivers. 



80 SMITH'S ESSAYS 

In view then, of the beauty, the usefulness and the 
grandeur of rivers, and their intimate association and re- 
lationship with whatever in the history and experience of 
man, he most may contemplate with satisfaction and pride 
it must be confessed and the confession may be excused, 
that there comes a lively pleasure with the hope that here- 
after, as long as men shall find delight in the varied land- 
scape, as long as the children of men shall revel in life and 
health, and as long as glad eyes shall be mirrored in glad 
waters, a new thought shall have been awakened in every 
dreamy, azure depth, and a new note in the soft music of 
every rippling, murmuring brook. 

Glaciers and Airstreams 

The principle of the double-spiral applies not alone to 
the movement of water, but likewise to that of all other 
fluids, and viscous semi-solids as well, when they are 
moving in channels. In the movements of glaciers the 
appearances are to a large extent misleading, and experi- 
mental proof is not so easy to obtain as is the case with 
water, but the principle that governs in both is essentially 
the same. 

When a flow of water has developed into a channeled 
stream, the small viscosity of the fluid allows the momen- 
tum of the surface to have nearly free play : hence the mo- 
tion of the upper stratum is increasingly rapid to the very 
middle of the stream, where as we have seen, the water on 
cross section is even heaped up into a ridge, and the sur- 
face broken up into wrinkles. If, h )wever, the banks of a 
stream of water are very gently sloped, the motion of the 



THE LAWS OF RIVER-FLOW 81 

spiral does not extend quite to the margin, but leaves a 
narrow strip next to the bank very slightly affected, and in 
eflFect constituting almost as much a part of the channel 
as of the stream. 

In glaciers this condition of the margins is much more 
marked and extensive, and also along the middle line of 
the ciu^rent there is a more or less extensive broad band 
that has no transverse nor oblique, but only a longitudinal 
movement. If as currently held by scientists, the semi- 
fluid condition of the ice in the ice river, is due to the 
pressure of the overlying mass on the parts beneath, it is 
obvious that this condition could not extend up to the sur- 
face, since the surface would be necessarilv free from down- 
ward pressure. The only pressure at the surface would 
be the lateral pressure due to oblique inward flow, and 
this would be supplem^ented to a certain extent by the heat 
of the sun whenever that might be operative. 

But in addition to the necessary absence of pressure at 
the free surface, the superficial portions of the glacier, in 
the middle as well as at the margins, is protected from the 
Sim's rays by the debris forming the central and lateral 
morains. It thus becomes more rigid even when exposed 
to the heat of the sun than it otherwise would be. 

The two semi-ellipsoids forming the active part of the 
glacier (Fig. 5) will not, therefore, as a rule, extend to the 
surface with full power: and as a consequence a more or 
less extensive area of surface ice will be left free from lat- 
eral motion as shown in the illustration. The inward 
movement of the upper surface of each cylinder will, how- 
ever, drag the less viscous surface ice obliquely downward 
and inward toward the middle of the surface of the glacier 



82 



SMITH'S ESSAYS 



with the result that innumerable fractures in the hard ice 
of the surface, will be made as it is pulled upon obUquely 




Fig. 5. 

A-— Unaffected ice at margin. 

B — Medium part miaffected by lateral morains. 

C — Center of cylinder. 

The arrows show the direction of spiral motion. 



by the more viscous and more rapidly-moving mass 
beneath. This would account for the pavement-like 
corned or mosaic appearance usually presented by the 
surface of glaciers. 

Rocks Rise to the Surface 



Rocks and other heavy objects dropped into fissures in 
glaciers, it is said, have been observed to rise to the surface 
at the edges further down in the course of the glacier. This 
fact would go to prove, for such instances at least, that 
the ice moves out at the bottom and upward at the 
margins. 

The fact maintained or conceded by all authorities, that 
the movement of glacier ice at the sides .and bpttom of the 



THE LAWS OF RIVER-FLOW 83 

channel is retarded, and that of the central portions is ac- 
celerated as compared with the edges, forces the conclu- 
sion that the double-spiral motion obtains also in glaciers. 
If there is retardation at the side it must be continuous and 
progressive: and if there is acceleration in the middle, un- 
less some new force is taken into account, it must also be 
continuous and progressive. 

The part of the glacier in contact with the channel walls 
or near them, must under progressive retardation, soon be- 
come entirely stationary, and if its place in the moving 
mass or column be not taken by ether and faster moving 
portions, moti( n in the entire glacier must of necessity 
eventually cease, if indeed, it could ever have begun. For, 
as shown in the case of streams of water when the outer 
parts become stationary from friction against the walls of 
the channel, the parts next within would become station- 
ary from friction against these, and so on until the entire 
mass should be brought to a complete standstill. 

On the other hand if only the middle is affected by 
accelerating forces, there is no reason why they should not 
continue to operate until this portion of the glacier should 
attain the speed of the most rapid river : and it would do 
so unless its acceleration were counteracted by inter- 
change with the retarded parts at the margin. 

Do Glaciers Erode Channels? 

It is not probable, however, that the double-spiral action 
in glaciers has ever been intense enough to inaugurate 
channel formation. There is hardly room for doubt that 
water initiated all the channels which now form the beds 



84 SMITH'S ESSAYS 

of glaciers, even if sub-glacial streams are not still the prin- 
cipal agent in the further erosion of their beds. 

We have seen that where water spreads out and flows 
over level land it breaks up into double-spirals whose 
distance from each other is proportional to the depth of 
water, and a channel is eroded for the meeting place of 
each pair of these spirals, that is for each double spiral. 
If ice were capable of eroding channels de novo, in the 
extensive plains over which ice caps once flowed for 
thousands of years together, these should be found cut 
into by numerous parallel channels, Nothing of the kind 
appearing we may justly conclude that flowing ice does 
not erode channels, but only follows them when already 
eroded by water. 

Streams of Atmosphere 

The application of the principle of the double-spiral 
to the movements of streams of atmosphere is self -sugges- 
tive: but owing to the limited friction among the parti- 
cles of air, as compared with those of water, the question 
is embarrassed with puzzling complications. This charac- 
ter of movement appears to be frequently exhibited in con- 
nection with summer showers, in regions where there are 
long, narrow valleys traversed usually by streams of water. 
It is a widespread popular behef , that streams of water at- 
tract rain, and it cannot well be denied that territory in the 
neighborhood of streams, is favored with more than its 
proportional share of summer showers. 

It is not, however, that streams or water courses actually 
attract rains, but that winds moving in line or nearly in 



THE LAWS OF RIVER-FLOW 85 

line with extended depressions, in which streams flow, take 
on the double-spiral or stream form, and the clouds are 
thus drawn into the middle, just as drift is drawn into the 
middle of a creek or a river. Winds along the St. Law- 
rence river have been observed to be carried several de- 
grees out of their course, when the general trend happened 
to be obliquely across the river valley. Close observation 
will doubtless show this to be a very common phenomena. 

A very significant illustration of the principle under dis- 
cussion has been reported to me by Captain John T. 
Campbell of Rockville, Indiana, a civil engineer, and a 
most intelligent observer. Captain Campbell, in a 
letter to the author reports that in the Wabash bot- 
toms near Rockville, the deflection of a creek from its bed, 
has left a deep ravine, very tortuous but somewhat parallel 
with the course of the river. It was noticed that when the 
river bottoms were overflowed and the site or line of the 
ravine was covered with w^ater to the depth of seven or 
eight feet, the drift which was quite abundant on account 
of the deadening of the timber along the river higher 
up, followed accurately the tortuous line of the ravine 
formerly the channel of the creek. 

This interesting observation not only gives strong proof 
of the double-spiral in streams, but also aptly illustrates 
the method by which rain clouds might be made to fol- 
low extended valleys, even when the course of such valleys 
might not be parallel with the movement of the wind. 

Blizzards and Texas Northers 

While the double-spiral is the necessary outcome of the 
flow of fluid in a channel, a single spiral may be produced 



86 SMITH'S ESSAYS 

by a single wall wherever a continuous stream of fluid 
moves in the same general direction, and is held against it 
so as to produce friction. This phenomenon is developed on 
a large scale wherever a vast movement of the atmosphere 
takes place along the side of an extensive mountain chain 
or range. Thus when an area of high pressure extending 
far to the north, compels a widespread movement of the 
atmosphere southward along the eastern slope of the 
Rocky Mountains, the mountain wall on the western side 
of the flow, acts as one side of the channel of an enormous 
river. The friction of the air against the sides of the moun- 
tain range causes it to be retarded and to rise up along the 
eastern slope of the range towards the summit. While 
the retarded air is moving out toward the mountain and as- 
cending it in this way, the air of the mid-current above, 
settles down to take its place: and since the upper air has 
out-traveled the lower strata, and has consequently come 
from points farther to the north, it is both colder and 
as a rule drier. It is true that the constant easterly cur- 
rent blowing from the west over the mountains, has a ten- 
dency to draw the air which is eastward of the mountains, 
up toward their summits, but it is mainly the friction of 
the atmosphere against the eastern slopes of the Rocky 
Mountain ranges that determines both the blizzard and 
the Texas norther. 

Practical Application of the Theory 

The application of the principles considered in this essay, 
may be of service in promoting the discovery of general 
formulas for calculating correctly the capacity of canals 



THE LAWS OF RIVER-FLOW 87 

for conveying water at various degrees of incline : of meth- 
ods for keeping irrigating canals free from intruding gravel 
and boulders as well as other like obstructions, where the 
water enters them from rivers : of methods for the eflBcient 
utilization of jetties for deepening the outlets of rivers, and 
for deepening the entrances to harbors with the aid of tidal 
waters. 

The question of this nature, which for the American 
people surpasses in interest and importance, is that of the 
control of the Mississippi river, though every country has 
occasion for the special application of measures of this char- 
acter. The problem of the Mississippi involves the consid- 
eration of three principal features, in regard to each of 
which there has prevailed much diversity of opinion. 
These features are the construction of jetties at the mouth, 
the erection of levees along its banks, and the maintenance 
of outlets in the upper part of the delta. 

The jetty system as at present in operation at one of the 
outlets of the Mississippi, stands approved throughout 
by the principle of the double-spiral : for it aims at the con- 
traction of the width of the stream of water flowing over 
the bars, so as to secure the proper relation of speed and 
depth and consequently the greatest erosive effect, where 
otherwise the tendency would be for the stream to widen 
at the expense of both speed and depth, or even still 
further to divide and form smaller channels. 

The depth limit to which any body of water flowing be- 
tween jetties can attain, is of course as in all other streams, 
the point at which the mass of accelerated water sinking 
down in the line of the current ceases to strike the bottom 
with suflicient force to effect erosion. The problem would 



88 SMITH'S ESSAYS 

be greatly simplified, if a river had but a single outlet, so 
that something like a head of water could be secured for 
lower stretches. This can in part be attained even where 
there are multiple outlets, by disposing the inlet of the 
jetties in such a way as to gather in as much of the flow 
as practicable, and then narrowing the inclosure further 
along toward the sea. 

A curved path for the channel convex on the right, as 
required by the deflection due to the earth's rotation, 
would perhaps be a wise provision. For a stretch of outlet 
of considerable length, the curved form would probably 
be of less advantage than in a short section of channel : but 
in the construction of channels of entrance into harbors , 
the curved form is probably the only feasible one. At all 
events it is certain that whether effected by accident or 
design, the only satisfactory measures for keeping clear the 
entrance to harbors by the utilization of tidal flow, have 
been based on this plan: as for instance the harbors of Dub- 
lin and Charlestown. 

Levees 

The question of levees is one that presents greater eco- 
nomic and financial than engineering difficulties. The 
levee system is in large measure based on nature's own 
plan: for as already pointed out, a river emptying into a 
shallow sea, will if it carry sufficient silt, build up banks 
for itself, and then throw up levees over these banks so as 
to limit, if not ultimately to arrest its own overflow. 

But nature contemplates a continuous levee, and the 
uniform overflow of a river even if not its complete re- 



THE LAWS OF RIVER-FLOW 89 

straint, and not the building up of such a wall as causes 
the accumulation of a large head of water, to be allowed to 
pour through at a few points and divert the water through 
open outlets to the sea. The indications for the conserva- 
tion of the channel in flooded streams would seem to be the 
placing of the levees as far back from the edge of the water 
as practicable, to make them broad and continuous, and 
to restrain all lateral outlets: then after a long lapse of 
time, probably measured by centuries, to open up new 
outlets on shorter lines to the sea: and finally after the 
lapse of ages, when the bed of the stream and its banks 
have been raised too high for the eflFectuation of flood 
control, to abandon the low^er parts of the delta region 
to be built higher by the deposit of silt from overflow. 

Lateral Outlets 

The propriety of constructing lateral outlets which shall 
lead off a part of the flood water of the Mississippi, and in 
like case of any other river, at some point above its mouth, 
with a view to diminish overflow or deepen the channel, 
has given rise to a great deal of controversy. But con- 
sistently with the principles here advocated, outlets would 
for the present prove futile or harmful according to their 
extent and the results they might be expected to accom- 
plish. 

They would prove futile unless they should succeed in 
changing the course of the river, so as to lead it bodily by 
a shorter route to the sea: for nature's rule is to carry the 
largest possible body of water by a single channel to the 
neighborhood of the sea filling up terminal outlets by the 



do SMITH'S ESSAYS 

way. If, therefore, lateral outlets should be kept perma- 
nently open, the main channel below them would contract 
to accommodate itself to the restricted flow. This would 
be promoted by the abundant silt which being found in 
the greatest proportion at the bottom of the stream, would 
remain in excessive quantity in the main channel. 

The Gulf Stream 

The gulf streams, so called because the first of these 
great ocean rivers to be observed, was discovered flowing 
out of the Gulf of Mexico through the straits of Florida, 
are not altogether of the nature of rivers, though their 
currents in parts of their courses are well marked off from 
the rest of the ocean. But since this is effected by walls of 
water, the friction must be relatively small, and the river- 
like action very limited. But even where the form or the 
order of movement of the mass of water and the amount 
of friction, are not such as to elicit the double-spiral, the 
molecular initiative of movement is of the same nature in 
both cases, since the same principles apply to the move- 
ments of all fluids. 

The principles involved in these vast movements of the 
ocean circulation, are perhaps easiest understood by anal- 
yzing the forces operative in their production, and by con- 
sidering them in detail. The main difficulty in their study 
is in ascertaining just how much of the movement is due 
to the trade winds, and how much to the interchange of the 
warm water of the tropics and the colder water of the polar 
regions under the modifying influence of the earth's rota- 
tion, a cause identical with that which produces the trade- 
winds. 



THE LAWS OF RIVERFLOW dl 

Let us first attempt to conceive what the movement of 
the waters would be in case there were no tradewinds nor 
any winds at all affecting the ocean circulation. In that 
case the w^ater would expand under the sun's heat, along 
the line of the equator, and the level of its surface would 
be raised, but the total weight over any given area would 
not be increased, and only the water near the surface would 
be made specifically lighter. 

There would take place then no adjustments of equilib- 
rium at great depths, as would be the case if the mass of 
the warmed water were made actually heavier. The por- 
tion of the water thus raised above the general level by the 
expansion would therefore flow off poleward since in that 
direction would be found the lower level. This would 
produce an area of lower pressure over the part from which 
the flow^ took place, and the colder water beneath would 
rise up to be warmed in its turn and to flow away in the 
same manner. 

As the surface water flowed poleward, it would be de- 
flected to the eastward by the earth's rotation, and the 
cold inflow along the bottom of the ocean would be de- 
flected west from the same cause, exactly in the way the 
planetary winds are affected. The waters corresponding 
to the tradewinds would be at the bottom of the sea just 
as the tradewinds are at the bottom of the ocean of the 
atmosphere. 

Effect of the Tradewinds 

But what would be the conditions if the tradewinds alone 
affected the movement of the water, and there was no other 



92 SMITH'S ESSAYS 

circulation of the sea than that due to their action? In that 
case the winds blowing in from both sides toward the equa- 
tor, would heap up the water along the line of the equator, 
and the weight or mass over any given area would be in- 
creased. This would result in a movement of adjustment 
of equilibrium extending possibly quite to the bottom of 
the ocean, for the heavier mass would settle down and dis- 
place the water beneath it. But how far poleward would 
this displaced water move before coming again to the sur- 
face .^^ It could not return to the surface except to flow 
back to the equator, until it had reached a point poleward 
of the tradewinds, and then it would rise to supply the 
depression caused by the removal of water toward the 
equator by the action of the tradewinds. 

In short there would be produced on each side of the 
equator and parallel with it, a vast revolving ellipsoid or 
cylinder with the free surface moving equatorward. But 
the oblique direction of the tradewinds would produce a 
westward flow of the water all along the line of the equator. 
Of course the whole of the water set in motion by the wind, 
could not be driven before it for any great length of time 
for otherwise, before being driven any great distance it 
must either attain to enormous speed or grow into a mass 
of enormous bulk. The actual condition would be that 
after attaining a slight elevation, the water would escape 
and be dissipated by an adjustive movement of equilibriun 
beneath in the manner already indicated. In the mean- 
time there would be generated in the water a steady flow 
to the westward. 

How would this flow be disposed of on meeting a conti- 
nental obstruction? Would it not turn back and move 



THE LAWS OF RIVER-FLOW 93 

toward the east, close along the poleward side of the trade- 
winds and thus set up a whorl or eddy extending east and 
west from continent to continent? And it is not easy to 
see how the flow could at any point be deflected from this 
eddy and move off toward the poles, the tradewinds alone 
being operative. 

It is the combination then of these two forces that pro- 
duces the ocean currents. The tradewinds hinder the pole- 
ward flow of the expanded surface water of the equatorial 
belt, but otherwise the planetary circulations of the air 
and water, as far as they coincide, supplement each other. 
The westward flow along the line of the equator is largely 
and may be mostly due to the action of the tradewinds, 
but the great poleward flow of the ocean currents are most 
probably almost wholly due to the planetary circulation 
of the water caused by the difference of equatorial and po- 
lar temperature, in combination with the earth's rotation. 

But the problem in its details is one of almost infinite 
complications and can be satisfactorily solved only by 
a long series of experiments and observations. 

The Flow of Water tn Closed Canals 

The flow of water in pipes or tubes and other closed canals 
could differ with such flow in open channels only in cases 
where such pipes or tubes were entirely filled by the liquid. 
If they were only partly filled, the flow w^ould be governed 
by the same law^s as flow in open channels. But when 
pipes are entirely filled with flowing water, the complete 
peripheral friction introduces into the problem a new ele- 
ment in the way of the disposal of friction. 



04 SMITH'S ESSAYS 

From a careful consideration of the forces in operation, 
it would be a logical deduction, that a fluid flowing through 
a tube completely filled, must break up into sections and 
move along one section following another, and each sec- 
tion as it progresses exfolding in front and infolding from 
the rear. The general movement of advance of the whole 
stream, however, would be much greater than the second- 
ary movements of the elements of the sections. 

We will first attempt to conceive single particles of the 
mass of water in a tube, moving in contact with the tube 
wall, and realize how they will deport themselves under 
the friction to which they would be subjected. In the first 
place, as the mass advanced, such particles would be im- 
peded and move on less rapidly than the central poi;tions. 
And since this retardation would be continuous, the par- 
ticles next the wall would move more and more slowly 
relatively to the central portions. As each particle or 
lamina of particles falls behind, the particles from within 
would be pressed outward to take their places in the pro- 
cession: and each particle so moving out would by its 
superior momentum, drive a slower moving particle away 
from the wall. As the slower one moved away it would 
be struck by a faster moving particle which would circle 
around it keeping on the outside of it, that is to say, on the 
outside of the circle in which the two would revolve. 

In this way progressively larger wheels or rolls would be 
formed until they would involve the entire diameter of 
the content of the tube. These wheels would gradually 
become symmetrical in their movement, since it will be 
found easier to move along in even ranks than separately, 
and they would roll along on the tube wall in the diree- 



THE LAWS OF RIVER-FLOW 95 

tion of the flow. The action would be very similar to 
that by which rolls of hay are formed when haycocks are 
dragged over a newly-mown meadow. 

This hoop-like or wheel-like movement must stop at the 
center of the tube, for there each wheel would meet the 
corresponding roll or wheel from the opposite side. This 
movement when completely established, would take form 
in sections having somewhat the shape of lemons divided 
into longitudinal sections, these sections revolving end- 
wise, the thick part narrowing to a sharp edge as it 
became the inside and moved rapidly, and again swell- 
ing out as before when it became the slow-mo\dng out- 
side. The middle part is made thin because the water of 
which it consists moves rapidly and the thin edge of the 
middle becomes thick when it has turned to the wall, for 
the reason that the water composing that part again 
moves slowly, and requires a larger area in which to move. 
But the actual conditions are yet more complex. 

If a colored liquid be injected intermittently into a 
stream of water flowing up through a glass tube, a menis- 
cus of the colored water will be seen to advance along the 
center of the tube, and as the colored water is passing off, 
the after part of it will be seen to be hollowed out or cup- 
shaped. That is, the clear water is now following with a 
meniscus projecting into the colored fluid just as the col- 
ored fluid advanced with a meniscus into the clear water. 

We are then forced to the conclusion, or at least justi- 
fied in concluding that water in tubes and other closed 
canals moves in sections the exact counterpart of a stack 
of thimbles arranged one within another, the small or 
pointed ends taking the direction of the stream-flow. As 



0/ SMITH'S ESSAYS 

these thimbles move on in a body, each thimble wall is di- 
vided into two laminae, an inner and an outer. The inner 
lamina or half of each thimble wall, moves forward and to 
the center of the tube and there after passing through the 
center of its own meniscus, folds back to become the outer 
lamina or wall, and then again the inner lamina when the 
large or concave end of the thimble-like section has been 
reached. 

The necessity of a constant interchange of position be- 
tween the particles next to the tube wall and those moving 
in the middle, is obvious to the slightest reflection. The 
particles next the walls are not only retarded but their 
retardation is continuous, and it necessarily follows that 
unless the relative position of these particles is changed, 
they must shortly become absolutely stationary : for when 
their motion is once quite arrested, the viscosity of the 
fluid will cause friction with the next layer within with 
ultimate total arrest of motion, and so on continously un- 
til the entire stream is brought to rest. 

Again, water flowing in a tube is found to flow faster at 
the center than at the circumference, there being between 
them a steady gradation of flow, the water at the center 
moving it may be, several times faster than that near the 
wall. Assume that when the water first enters the tube 
all the molecules have an even start : that at the end of ten 
feet the center is moving three feet per second, and the 
portion next the wall is moving one foot per second, w^hat 
is there to prevent the water in the center at the end of 
twenty feet from moving at the rate of six feet per second, 
or nine feet per second at the end of thirty feet or from 
eventually attaining the speed of a cannon-ball? 



THE LAWS OF RIVER-FLOW &)5 

) 

The fact is, however, that after a few seconds of flow, 
kinetic equihbrium is attained, and thenceforth the speed 
of each part is uniform, and the relative speed of the outer 
and inner portions remains the same. There is then neces- 
sarily taking place, a constant interchange between the 
more retarded outer and the less retarded inner portions 
in the flow of fluids through every closed canal. 

A series of experiments and observations made by Mr. 
Van Sendenberg, a distinguished civil engineer of De- 
troit, has a strong bearing in support of this view\ These 
experiments were made with water flowing through a pipe 
twelve feet in diameter, with both ends submerged. Into 
this pipe he injected a solution of cosine, and found that 
after the water had flowed one-fourth of a mile, the cosine 
was still confined to a section of the pipe not more than 
nine feet long. The principle of this case no doubt ex- 
tends to the flow of liquids in all tubes, and the result of 
the experiment would indicate that the rotating or infold- 
ing and exfolding segments previously spoken of, have a 
length of about three-fourths of the diameter of the par- 
ticular tube. 

The speed of movement of water in tubes is proportional 
to the completeness of this organization into segments. It 
is for this reason, probably, that w^ater will flow faster in 
tubes with angles, than in tubes with steady curves. 
Movement in a curved tube of necessity continually dis- 
arranges the flow in organized segments, for by making one 
side of the segment longer than the other, there is required 
a continual readjustment. On the other hand, in a tube 
consisting of straight stretches and angles the water will 
have its organized movement broken up only at the sharp 



98 SMITH'S ESSAYS 

bends; while the roIKng segments will not be interfered 
with in the straight stretches. 

This rolling motion of fluids can be observed in almost 
any smoke-stack of considerable height, and especially in 
circular ones, when an abundant flow of smoke or steam is 
taking place from them. From all such pipes or chimneys, 
smoke and steam escape in rolls or volumes. And it can 
easily be noticed that the rolling is an outward or unfold- 
ing one for each escaping section of the kind that has been 
contended for in the case of water and other liquids. 

If it be objected as has been done, that the resistance or 
friction of the surrounding atmosphere exerted upon the ex- 
ternal surface of the stream of smoke or steam cs>uses it to 
move off in volumes, the answer is, that if the friction of 
the surrounding atmosphere, causes the rolling movement 
in the smoke column after it escapes from the chimney 
surely the friction of the walls of the chimney or smoke- 
stack would cause a like rolling before its escape. 



THE FUNCTIONS OF THE SPHERIC WEDGE 

OR 

THE PHILOSOPHY OF FLUID EQUILIBRIUM 



INTRODUCTORY 

The principle of the hydrostatic paradox was first enun- 
ciated by Blaise Pascal about a century and a half ago 
and almost at once met with a general acceptance, which 
may now be said to have become fairly universal. 

As extended to the entire subject of the equiHbrium of 
fluids, it becomes one of the most important and widely- 
appHcable principles in physics. 

The author in many efforts made to reduce the princi- 
ple to a final analysis found himself unable to attain this 
or indeed even to approach it, until there occurred to him 
the expedient of the liquid or fluid wedge, which is really 
but a secondary application of the wedge principle as 
manifested in the action of the molecule when regarded 
as a spheric wedge. 

When the attempt was first made in a medical work of 
the author entitled ''Obstetric Problems," to set forth the 
principle, and later when its fuller explanation was at- 
tempted in the article entitled, ''The Functions of the 
Fluid Wedge," embraced with other essays in the book 
published by the author and entitled "Philosophy of 
Memory and other Essays," the ultimate factor supplied 
by the spheric wedge had not been fully conceived though 
dimly apprehended. 

In the recognition of the principle of the spheric wedge 
supplemented with the conception of the bent molecular 
tube, it is confidently believed a final analysis of the mech- 

101 



102 INTRODUCTORY 

anism of fluid equilibrium has been reached; and that on 
careful examination it will clearly appear that there is no 
essential difference between the balancing of solids and the 
balancing of fluids as expressed by the term, * 'equilib- 
rium. " 



THE FUNCTIONS OF THE SPHERIC WEDGE 

OR 

THE PHILOSOPHY OF FLUID EQUILIBRIUM 

Something over a century and a half ago, Blaise Pascal, 
a famous French scientist, announced the discovery of a 
principle in the equihbrium of fluids which he denominat- 
ed the "Hydrostatic Paradox." 

The statement of the principle as defined by that 
great philosopher is embraced in the expression 
that any quantity of water or other fluid however small 
may be made to balance any weight, however great, or 
any other quantity of fluid, however large. An apt illus- 
tration in popular use is the example of the teapot, in 
which the tea in the spout stands at the same level as that 
in the body of the vessel. As another illustration of the 
principle, it is often remarked that a child by thrusting 
its finger into a connecting crayfish hole can raise the 
level of the water of an entire ocean. 

The vogue of the so-called principle announced by Pas- 
cal has steadily expanded, until now the term Hydrostatic 
Paradox appears in every comprehensive dictionary and in 
nearly every encyclopedia and text-book of physics in the 
entire world. Yet notwithstanding its world-wide vogue, 
notwithstanding the uncounted millions of books in which 
the term appears, and the innumerable schools, colleges 

103 



104 SMITH'S ESSAYS 

and universities in which the doctrine is taught, it is here 
proposed to demonstrate conclusively that there is no such 
principle hmited exclusively to fluids or hquids, or pertain- 
ing to them any more than to solids. In short it is easily 
demonstrable that the principle is neither exclusively 
hydrostatic nor at all a paradox, however much it may 
seem so on superficial examination. 

A paradox is something that appears to be false and yet 
is really true. The purpose of this discussion is by a care- 
ful analysis to show that the alleged principle as described 
in the term paradox, is not only not true but does not 
even seem to be true when rightly understood. 

If the finger or a rod be thrust into a cup filled with 
water the liquid will rise up and portions of it will flow out 
over the brim of the vessel. 

Manifestly the water thus displaced is not lifted up di- 
rectly, but only in an indirect manner: and if indirectly 
then necessarily this is accomplished through the instru- 
mentality of one of the mechanical powers. By which of 
the mechanical powers is it so raised? 

Strictly speaking, there are but two mechanical powers, 
namely: the lever and the inclined plane. The lever, be- 
sides the different forms it takes as such, is also modified 
into the wheel and axle and the pulley. The inclined plane 
is modified into the screw and the various forms of wedges 
or moving inclined planes. 

In the raising of the water in the example cited, there is 
evidently no form of leverage involved. Either, then, the 
water is lifted up by some form of inclined plane or we have 
here to do with some form of mechanical power not 
hitherto described. A Uttle reflection, however, will clearly 



THE FUNCTIONS OF THE SPHERIC WEDGE 105 

show that the elevation of the water is actually effected by 
means of the moving inclined plane or wedge, which in this 
instance is primarily the molecule functioning as a spheric 
wedge. 

Sir Isaac Newton, in opposition to the views of some 
ancient philosophers, supposed that atoms are perfect 
spheres and there is now probably more reason for believ- 
ing such to be the case than there was when he put forth 
that opinion. But whatever the shape of atoms may be, 
molecules being made up of varying aggregations of atoms, 
could be strictly of a spheric form in only a very small pro- 
portion of cases. Be this as it may, however, both mole- 
cules and atoms may for the purpose of performing the 
functions of spheric wedges, be regarded as practically 
constituting spheres . 

Both molecules and atoms are surrounded on all sides 
by a field of repulsive force which prevents them from 
coming into immediate contact, and which may be rightly 
regarded as consisting of lines radiating from their centers. 

If now the radiating lines of this repulsive force be con- 
ceived to be cut off all around at an equal distance from the 
surface of the atom or molecule, the resulting body inclosed 
within the cuts would form practically a sphere, the in- 
equalities of the smaller body, that is the central atom or 
molecule, not being noticeable on the larger one formed by 
the clipping off of the Hues of force as described. At all 
events, such a body will be sufficiently rounded to consti- 
tute it an effective spheric wedge. 

Therefore when an atom or molecule is forced in between 
two or more other atoms, molecules or other bodies, it will 
act as a wedge in separating them : and this too as a wedge 



106 SMITH'S ESSAYS 

of the utmost sharpness or smallness of the angle of incKne 
as its base which is found at its equator is gradually 
reached and begins to fulfill its wedge function. 

Assuming then that atoms and molecules have respec- 
tively the properties and functions of spheric wedges, we 
may for convenience of comprehension and application, 
conceive them as having the actual shape and proportion 
)f wedges when performing the wedge function. That is 
to say, we may consider each atom and each molecule as 
presenting in every direction the apex of a prism. 

Transmission of Pressure by Spheric Wedges 

As an aid to the easier understanding of the principle, 
we may conceive of atoms and molecules as being enlarged 
to the size of marbles, possessed of perfect rigidity or per- 
fect elasticity and moving freely, that is absolutely with- 
out friction. The behavior of a mass of such spheres un- 
der the conditions assumed, is made manifest in the follow- 
ing illustration. (Fig. 1.) 

In such a mass or group, every ball tends to press into 
the interspaces of the balls immediately below it and to 
wedge them apart. Each ball so pressed horizontally tends 
to enter the interspaces of the balls at its sides and to 
wedge these balls apart, and also to press upwards the 
balls lying above its horizontal plane, and downward those 
below that plane. In short it tends to enter every inter- 
space to which it is contiguous. 

Every layer of balls lends its weight to that of those 
above it, so that in the direction from the top toward the 
bottom of the mass, each layer is pressed upon more 



THE FUNCTIONS OF THE SPHEHIC WEDGE l07 



heavily by the weight of one layer than is the layer above 
it. And since the pressure from above is met by a counter 



S8M 

oooo 

ooooo 



Fig. 1, 



pressure or reaction from below that is equal to it, the 
balls from the direction of the bottom of the mass press 
upward with a like effect of wedging apart those above 
them as well as those at their sides, and those below them 
if there happen to be any so placed. 

Action of Combined Wedges 

The simple spheric wedges described may be correctly 
assumed to have distinctly the form of simple wedges or 
prisms, and may also be conceived as being combined into 
larger aggregates each such larger aggregate preserving 



108 SMITH'S ESSAYS 

the same shape and form as each of its smaller constit- 
uent wedges. This compound wedge, having the same 
shape and proportions as its c )nstituent wedges, will act 
in identically the same way as would one of these con- 
stituents before the forming of the combination. 

In the annexed illustration (Fig. 2)f )ur wedges are rep- 
resented as combined into one, and that too in such a way 
as that the resulting aggregated wedge has for all practical 
purposes the same shape and relative proportions as each 
of its constituent parts had before the combination. 




Fig. 2. 

Its action will therefore be along the same lines as that 
of one of the molecular or atomic wedges entering into its 
structure. These aggregations may be conceived as in- 
creased in size until for all practical purposes of wedge 
action, every confined mass of fluid is divided into two 
equal wedges with their bases turned in opposite direc- 
tions. (Fig. 3) 



THE FUNCTIONS OF THE SPHERIC WEDGE 109 

Furthermore, this arrangement is in fmiction, actually 
accomplished in liquids and fluids perpendicularly, hori- 
zontally and obUquely at the same moment of time. Nor 




Fig. 3. 

is this an unreasonable view or a difficult conception, when 
we consider the facihty of adjustments among the parti- 
cles of fluids, and that such a range of function is indis- 
pensable for meeting the requirements of fluid or liquid 
pressure. 

The Perfect Wedge 



It may be of some assistance in gaining a clearer view of 
some of the questions with which we are about to deal, to 
ascertain as far as we may, the shape that a perfect wedge 
must assume. And in attempting this we shall realize 
probably with some surprise, that the two inclined planes 
constituting a wedge and the many constituting a cone, 
can have but one angle of incline if they are complete and 
continuous, unless there should be a difference in the size 



110 SMITH'S ESSAYS 

of the molecules or atoms entering into the same wedge or 
cone. 

Thus taking the thickness of the individual molecule or 
atom as constituting the thickness of the edge or point of 
the wedge or cone, (Fig. 4) the next degree of thickness 
cannot consist of less than two atoms, and this arrange- 
ment must allow the jutting over of half an atom as in the 
illustration. 



A 



Fig. 4. 

The third rank must have three molecules, the fourth, 
four, the tenth, ten and so on indefinitely. This would 
give to the planes an incline of about 45 degrees, and the 
resulting wedge would have the form of an equilateral 
triangle. A wedge that does not continuously increase in 
thickness must be regarded as simply a shaft in the sections 
or stretches where there is no increment : and the two sur- 
faces of a wedge that do not approach each other at an 
angle of 45 degrees cannot consist of perfect planes. 

It is true that for all practical purposes of mechanical 
action a wedge may be constructed of any degree of in- 



THE FUNCTIONS OF THE SPHERIC WEDGE 111 

cline : but a plane in which there is no break in the uniform 
succession of molecules cannot be met by another like plane 
at a sharper angle than 45 degrees and at the same time 
inclose a complete or perfect wedge: and this is probably 
the shape of the wedge composed of aggregated molecules 
that is employed in effecting fluid equilibrium. 

Limit of Intensity of Horizontal Pressure 

Having developed the proposition that the molecules or 
atoms composing a fluid, may and do act as wedges either 
separately or in aggregations of any size, from that of the 
ultramicroscopic to wedges of half the size of the mass of 
fluid into the formation of which they enter, and in every 
possible direction at the same moment of time, we may now 
proceed to ascertain the limit of horizontal or lateral pres- 
sure possible for each wedge acting under a given unit of 
force. 

Let us conceive a row of blocks absolutely rigid or per- 
fectly elastic and moving freely, or wholly without fric- 
tion, laid across the floor of a room and extending from 
wall to wall; and then let us suppose a wedge of sujEcient 
weight to exert a lateral pressure of one pound, to be let 
press into one of the interspaces of this row. The result 
would be that the wedge would cause a force or pressure 
of one pound to be exerted by every block of the entire 
row against those in contact with it, and a like pressure 
against the walls of the room. 

If now a like wedge be inserted into every interspace in 
the entire row of blocks and left free to operate, each of its 
own weight, no greater force than one pound would be ex- 



112 SMITH'S ESSAYS 

erted at any point in the line. All the horizontal pressure 
possible to be effected by such wedges acting of their own 
weight, would be that of the one wedge first to enter. In 
order to perceive clearly that this must be the case, we have 
only to consider that after the blocks have been pressed 
against each other throughout the entire row with a force 
of one pound, another wedge cannot of its own weight, en- 
ter any of the interspaces to begin horizontal pressure, un- 
less it can first exert a greater pressure or separating force 
than one pound. 

Or to illustrate in still another form; let us suppose a man 
to be pushing a rod across a room against an opposing wall, 
with a force of exactly ten pounds. Next conceive the rod 
to be cut in two, and a second man placed in the middle, 
pushing against the cut ends with either hand with a force 
of ten pounds, or repeat this again and again, and still 
there would nowhere be exerted a horizontal or lateral 
pressure greater than ten pounds. 

Again we may assume that a sphere of the size of the 
earth, or even Aldebaran, is covered with billiard balls 
absolutely rigid or perfectly elastic and moving freely, and 
then that a single other billiard ball of the same kind, ca- 
pable of exerting by its own weight, a horizontal pressure 
of one ounce, is let into one of the interstices of this layer. 
The result would be that every ball in the vast expanse of 
the layer would be pressed against every other ball in con- 
tact with it horizontally with a force of one ounce. Nor 
would the force of horizontal pressure be increased though 
a like ball were of its own weight let into every interspace 
in the entne layer. 

The significance of this demonstration is that a single 



THE FUNCTIONS OF THE SPHERIC WEDGE 113 

molecule of water, entering of its own weight as a spheric 
wedge, into an interspace in a layer of other molecules of 
water, as extensive it might be as the surface of the entire 
earth or the largest star, would exert all the horizontal 
pressure possible to be exerted by like molecules function- 
ing as spheric wedges, even though they might enter into 
every interspace of such layer. 

It means, furthermore, that all the lateral or horizontal 
pressure possible to be exerted in the entire mass of an 
ocean, or in the largest liquid or fluid sphere, would be and 
is, that of a single molecule entering as a spheric wedge 
into an interspace in each layer of molecules, while pressed 
upon by a coliunn of other molecules extending from its 
base to the free surface of the mass. Nor would a sepa- 
rate column be necessary for each layer : since while a mole- 
cule is acting as a wedge for one layer and exhausting its 
separating force of horizontal pressure for that layer, it can 
still in connection or conjunction with the molecules against 
which it is pressing laterally and with which it is in contact, 
exert its direct gravitational force upon the wedging mole- 
cule immediately below it. 

It must therefore result, that in a perpendicular tube 
containing only a sufficient number of molecules to admit 
of a single molecular interspace in each layer, all the hori- 
zontal force will be exerted that is possible at any given 
level in the largest body of fluid, the particles of such fluid 
being in each instance assumed to act of their own weight. 

Having proceeded thus far in the exposition of the theory 
of the wedge action of the molecule or atom and its homo- 
morphous aggregates, we may now enter upon a considera- 
tion of some of the numerous appUcations of the principles 
involved. 



114 SMITH'S ESSAYS 

Why a Flattened Tube Becomes Round 

It is a matter of common observation that if water or 
other fluid be forced into a flattened flexible tube, such as 
a section of rubber hose for example, the tube will take on 
the form of a cylinder. The reason given for this in the 
explanation most commonly offered, is that the circle em- 
braces the largest possible area for a given extent of boun- 
dary, and that the cyclinder has the largest content for a 
given extent of surface. 

This explanation is the true statement of a demonstrat- 
ed fact, but it does not in any degree attain to an ultimate 
analysis of the physical principles involved in the problem. 
The true explanation is based on the action of wedges of 
differing length and differing degrees of acuteness. And 
here, for the facilitation of the understanding of the matter 
we are constrained to invoke the notion of the aggregate 
or combined wedge, to which reference has already been 
made. 

If a quantity of water in a flattened flexible tube be con- 
ceived to be laid off into wedges with their bases of uniform 
thickness, and their apices meeting in the middle as in the 
cut, (Fig. 5), it is obvious that the wedges A and B, laid off 
in the largest diameter of the tube, will be longer and there- 
fore more acute than C and D laid off in its smallest diam- 
eter. 

It is manifest also that these wedges, though consisting 
of water, will insofar as the transmission of force is con- 
cerned, act exactly as solid wedges. For each wedge, 
while supported and held in place and form by the wedges 
W and W and the vessel wall, will in turn lend to the 



THE FUNCTIONS OF THE SPHERIC WEDGE 115 

wedges W and W and the vessel wall exactly as much 
support as it receives from them. 




Fig. 5. 

Let pressure now be made upon all the wedges figured 
in the illustration and to the same extent, say by forcing 
water into the hose or other pipe, under pressure. Then, 
since the wedges A and B are more acute than C and D, 
they will advance more readily under equal pressure. The 
result will be that C and D will be forced back by the re- 
action, carrying before them the flattened sides of the tube 
wall until all the wedges become of equal length and the 
tube becomes a cylinder. 

Why Soap Bubbles and Raindrops are Spheres 

The tendency of air bubbles and drops of rain or other 
liquid to take on the spheric form, must have been one of 
the earliest observed of physical phenomena. Yet no ex- 
planation of the mechanism involved in the process has 
hitherto been offered insofar as the author is aware, unless 
certa,in mathematical demonstrations based on surface 



116 SMITH'S ESSAYS 

tension might be so regarded. It is no explanation of the 
phenomena to say that the flattened sack takes the form 
of the sphere under internal fluid pressure because the 
sphere has the largest content for a given superficies, any 
more than is the like statement made in the instance of the 
tube. On the hypothesis of the liquid wedge, however, 
we are afforded a logical, simple and complete explanation, 
based on the elementary principles involved in the prob- 
lem. 

For the purposes of illustration we may now regard the 
previous drawing (Fig. 5) as representing, instead of the 
end of a flattened tube, the surface of a section of a closed 
sack, such for example, as a toy balloon; this sack to be of 
such construction as to be susceptible of expansion into a 
sphere, but as yet only partly filled and therefore some- 
what flattened. Instead of the simple wedges we had in 
the tube, we shall now in the sphere have cones with their 
bases at the circumference and their apexes at the center 
of the mass of the fluid. As in the case of the wedges, 
these cones support each other mutually, and move upon 
each other practically without friction. 

As we proceed to subject the cones to pressure by forcing 
fluid into the containing envelope the longer cones A and 
B being more acute and having the same area of base as 
C and D will advance more easily and rapidly. And since 
all the longer and more acute cones will advance more 
readily than the shorter and more obtuse ones, the latter 
will be forced to recede from the center, carrying the wall 
of the envelope before them, until all become of equal 
length and equal volume. Equilibrium will then have 
become complete and the inclosed mass a perfect sphere. 



THE FUNCTIONS OF THE SPHERIC WEDGE 117 

But the force that determines the sphere is not always 
exerted from without, unless, indeed, it should develop that 
gravitation is a push and not a pull. In the formation of 
the soap bubble, the power that drives the constituent 
air-cones, is derived from surface tension inherent in the 
liquid envelope and causing it to contract on its content. 
The case of the toy balloon is very similar, the power in 
both cases acting either directly on the bases of the cones, 
or indirectly on these through the pressure of the contain- 
ing envelope. 

But in the case of the raindrop the conditions are some- 
what different. Here, instead of a pressure from without 
acting upon a fluid confined in a containing envelope, we 
have a mass of liquid free in space, but with its particles 
subjected to mutual gravitational and cohesive attraction. 

In this case the extent of the attraction will be regulated 
or gauged by the angle of incline of the surface of the cones. 
The longer cones here having the same angle as the shorter 
ones, will have the greater mass and will consequently be 
drawn with the greater force toward the center: and this 
will continue with the necessary readjustments until the 
mass becomes a sphere. 

Balancing of Liquids in Connecting Chambers. 

The principles upon which is based the balancing of li- 
quids in connecting chambers, has hitherto proved to be 
one of the most puzzling questions in the dynamics of 
fluids. For a century and a half, or ever since its first sug- 
gestion in a scientific way by Ambroise Pare, as the * 'Hy- 
drostatic Paradox, " it has been set forth in untold millions 



118 SMITH'S ESSAYS 

of books to puzzle untold millions of students, and to baf- 
fle untold thousands of teachers. 

It is here proposed to demonstrate conclusively that a 
hydrostatic paradox does not exist, and that the principles 
upon which the so-called problem is based, v/hile incontest- 
ably true, are neither exclusively hydrostatic nor at all a 
paradox, but apply as well to solids as to liquids or fluids. 

But before entering upon a consideration of this branch 
of the subject, it would probably not be effort misspent to 
attempt to make plain to the non-scientific reader the 
meaning and bearing of the term ''lines of force" as relat- 
ing to the action of the wedge, whether liquid or fluid. 
Line of force means simply the direction in which an im- 
pulse of force tends to expend itself, or a wave of pressure 
is exerted. On a plane surface the reaction is always per- 
pendicular to such surface. 

In the case of the fluid or liquid wedges or cones into 
which a liquid mass may be conceived to be divided, and 
which by mutually and equally sustaining each other, act 
exactly as solid wedges would act, the lines of force will 
take direction at right angles to the existing planes. The 
mean direction, then, of all the lines of force in a mass of 
liquid will be at right angles to the two contiguous plane 
surfaces of two wedges whose bases are coextensive with 
any two opposite surfaces of the mass. 

The reactions of any two wedges, therefore, into which 
a mass either solid or liquid may be divided or conceived 
to be divided, being at right angles to their planes, will off- 
set or counteract each other, and thus the reactions will 
be at right angles to the opposite surfaces of the two wedges 
in the same way and same degree as if they consisted of 



THE FUNCTIONS OF THE SPHERIC WEDGE 119 

solid material. Then, since a fluid mass actually functions 
as a collection of wedges or prisms acting in every possible 
direction at the same moment of time, the pressure of 
a fluid against its restraining walls, will be everywhere at 
right angles to those walls. 

Or again we may conceive the surface or boundary of 
a mass of fluid to be everywhere occupied by the base of 
a wedge either molecular or aggregate, with its axis at 
right angles to such surface or boundary, and here again 
the pressure must be at right angle to this surface or 
boundary. 

Balancing Columns 

In order, however, to be able to comprehend with great- 
er facility the mechanism of the accomplishment of equilib- 
rium in fluids, and to make more clearly manifest that the 
principle is essentially identical in fluids and solids, it 
becomes necessary to form a conception of another and 
related process through which the level or equilibrium of 
fluid masses is attained, and also maintained when once 
accomplished. This process is the balancing of atoms, 
molecules and other freely-moving spheres, in pairs of 
columns. 

We may begin the study of this proposition by consider- 
ing the behavior of balls of any kind or size, occupying the 
two legs of a bent tube where the legs of the tube are di- 
rected upward. Let it be assumed that such a bent tube 
(Fig. 6) having its legs directed upward, is filled with bil- 
liard balls, or any other balls perfectly rigid or elastic and 
moving without friction. 



120 SMITH'S ESSAYS 

Obviously the balls would under such conditions, seek 
and maintain the same level in the two legs of the tube. If 
now instead of balls of the size of billiard balls, we conceive 
the contents of a tube to consist of single columns of 




Fig. 6. 



molecules of water or other liquid, the result will be iden- 
tical. Under like conditions the molecules will rise to the 
same height in the one leg as in the other, and then the 
content of each leg will exactly balance that of the other. 
These assumed conditions fairly represent the constitu- 
tion and behavior of every mass of liquid, and only in a 
less degree that of every fluid mass. Every such mass may 
be regarded as in effect consisting of bent tubes with their 
legs directed upward, and arranged in such a manner that 
the column of molecules in one leg exactly balances the 
column in the other leg. The walls of each of these tubes 
are assumed to be constituted of the molecules or atoms 
surrounding each such balancing column. It thus hap- 
pens that at one and the same time, every column of mole- 



THE FUNCTIONS OF THE SPHERIC WEDGE 121 

cules entering into the formation of a mass of liquid or 
fluid, constitutes the content of one leg of a bent tube ex- 
tending from the free surface to the bottom of such mass, 
and a part of a tube wall for every other column with which 
that column is in juxtaposition. 

As already indicated this description does not express or 
strictly apply to the actual arrangement, but it does apply 
strictly to the mean or resultant of the actual structure and 
function, or the average outcome of the forces and elements 
in operation. 

The strength of the walls of these tubes, that is, the 
amount of support which they can give to their content, is 
determined and fixed by the force of the horizontal wedge- 
pressure of a single molecule of and for each molecular 
layer of the whole mass in which such tubes exist, such 
molecule operating as a spheric wedge in the manner al- 
ready described. 

And yet, though the strength of the tube walls is sup- 
plied and regulated by the horizontal pressure of a single 
molecule for each molecular layer of every entire given mass, 
as before described, this support is nevertheless exerted 
through all the molecules surrounding the column. There- 
fore, when at any point or on any side of a column the sup- 
porting mass is withdrawn, or its support in any degree 
weakened, the walls of every tube whose support is thus 
withdrawn are weakened and will yield one after another. 

To the extent of this withdrawal of support and con- 
sequent w^eakening of the tube walls, their contents 
escape, so to speak, and the columns settle down until 
a new level is reached, and one that can be maintained 
by the remaining pressure. 



H2 SMITH'S ESSAYS 

It may be objected, however, that if a third leg be added 
to the bent tube connecting with it at its lowest point, the 
column in the three legs would still find and maintain a 
common and uniform level, notwithstanding the absence 
of pairs: and the objection would deserve consideration. 

We could in such a case meet the requirement of pairs, 
only by conceiving the molecular columns as being divided 
into and acting by halves. We should then have six 
columns out of which to form potential pairs for mutual 
balancing. 

Let three tube legs of the character in question be desig- 
nated a, b and c, (Fig. 7), and occupied by frictionless and 
perfectly elastic or rigid billiard balls, a, to the height of 
six inches, b, to the height of nine inches, and c, to the 
height of twelve inches. 

C 




Fig. 7. 

Obviously under such conditions, a ball from c would be 
forced by the pressure into the line connecting a and b, and 



THE FUNCTIONS OF THE SPHERIC WEDGE 123 

wouJd push the ball it came in contact with, in the direc- 
tion of a, or b, according as it happened to impinge on one 
or the other side of the center of such ball. Say the dis- 
placed balls move uniformly toward b. When the balls in 
b attain the same level with those in c, no more could be 
pushed in that direction. Then a ball would be pushed 
into a. If that ball came from b, and disturbed the bal- 
ance, the next must be pushed in from c, and then another 
from b, and so on until the same level should be reached in 
aU. 

If a ball coming into the crossing should strike another 
at the exact center, it might hold it in place and arrest the 
movement. But this could not happen one time in a mil- 
lion if ever, under the assumed conditions of absolute free- 
dom from friction. 

While this may not be easy to conceive clearly, its exact 
counterpart may be found in the balancing of objects un- 
der the principle of the lever. Thus, if a platform were 
surmounted on a pivot or suspended by a cord placed at 
its center and three men then placed on it in such a way 
that they would remain in perfect counterpoise, it could 
not be doubted that the balancing was effected by means 
of pairs, notwithstanding that the pairs must be had from 
the three individuals. 

The Hydrostatic Paradox 

This preliminary discussion brings us into a favorable 
position for the direct consideration of the hydrostatic 
paradox so-caUed. The proposition of the hydrostatic 
paradox is usually stated in one of the following forms: 



124 



SMITH'S ESSAYS 



*'Any quantity of water however small, can be made to 
support any other quantity, however large" or ''any 
quantity of water however small can be made to support 
any weight however large.' ' 

The operation of the principle may be Olustrated by an 
apparatus like the one shown in the annexed drawing. 
(Fig. 8) This apparatus consists of a long narrow pipe 



£L 



W 



B 



Fig. 8. 



A B, communicating with a vessel C D, into which is fitted 
an air-tight, movable top. 

Let C D be loaded with the weight W. If water be now 
poured into the pipe at A, water will enter the vessel C D 
and thus W will be raised: and this will be the case even 
though W were a continent floating on an ocean and A B 
no larger than the cavity of a microscopic tube. 

The weight which can be raised in this way, may be de- 
termined by calculating the relative areas of horizontal 
section of A B and C D. Thus suppose the horizontal 



THE FUNCTIONS OF THE SPHERIC WEDGE 125 

section of C D is 100 times that of \ B, then the weight 
which can be raised, will be 100 times the weight of the col- 
umn of water in the pipe above the level of the water in the 
vessel C D . 

Now if the contention herein maintained, that the col- 
umns of molecules in liquids and fluids balance each other 
in pairs and only in pahs, is correct in principle, we can 
most confidently assert that the water in the small tube, 
A B does not counterbalance the water in C D, nor that 
and the weight W; but only an equal number of columns 
of molecules, either mutually in A B, or else in C D. 

Furthermore, if one or more columns of molecules be 
required to be taken from C D to complete the pairs for 
those in A B, these columns will still balance each other 
in pairs. That is, the longer column in A B will form a 
pair with the shorter one in C D for, notwithstanding the 
columns in C D are the shorter, they are made equal in 
weight with those in A B by the pressure exerted on each 
of them by the weight W. 

The greater height of the columns in A B, serves only 
to indicate the height to which the columns in C D would 
rise, were their height proportional to their ot\ti proper 
weight added to that part of the weight W superimposed 
upon them: that is, the height to which they would rise 
if W were changed into water. 

It is simply a case of ordinary fluid equilibrium. The 
column in A B rises exactly to the level to which the whole 
connected mass would rise if it consisted whoU}^ of a homo- 
geneous liquid or fluid. Furthermore, if a solid rod of 
equal specific weight with the water in A B and moving 
without friction, were substituted for it, the pressure in 



126 SMITH'S ESSAYS 

C D and A B would remain the same throughout for cor- 
responding points. 

We have seen that a single solid wedge, entering into an 
interspace in a row or layer of solid bodies, and a single 
molecule entering as a spheric wedge into a fluid layer, will 
exert all the lateral or horizontal pressure possible to be ex- 
erted by wedges of like size and weight in such situation. 
We have also seen that a single molecule for each layer of a 
fluid mass, with a column of molecules resting on that 
molecule and extending from it up to the free surface, ex- 
erts all the unsupplemented horizontal force or pressure 
possible to be exerted in the entire mass, and that a mole- 
cule while acting as a wedge for one layer, can at the same 
time act as a wedge-driving weight for those below it. 

To form a ring of balls or spheres around another 
sphere of equal size, requires six such spheres placed 
around the seventh, all being in mutual contact. To con- 
stitute a composite column of spheres out of simple ones 
would require six simple ones placed around a seventh 
all in mutual contact. It would follow then, that a col- 
umn of liquid or fluid molecules having no more than 
seven absolutely rigid and frictionless molecules to each 
layer or cross section, would be suflScient to exert the full 
extent of horizontal pressure possible inany mass of liquid, 
or fluid even though as vast as Arcturus or Aldebaran. 

It is said that in order to be visible with the aid of the 
most powerful microscope, a disc should consist of more 
than 50,000 molecules, while few men can see with the 
naked eye, a disc containing less than 4,000,000 of these 
tiny bodies in one of its layers. 

Assume, then, that a column of molecules composed of 



THE FUNCTIONS OF THE SPHERIC WEDGE 127 

seven to each layer is sufficient for the exertion of all possi- 
ble lateral pressure in any mass of liquid, it follows that 
700 of these composite columns would have to be combined 
into one in order that a cross section might be seen with a 
microscope. 

Since then, a column so diminutive exerts or may exert 
the greatest degree or the highest intensity of lateral pres- 
sure possible to any number of such columns, how are we 
to localize the particular composite or compound column 
that is operative in any particular case. Compared with 
such a column the water in the connected tube in the figure 
and that in the body of the vessel are alike fairly oceans. 

Again; we have seen that if from any mass or body of 
water in equilibrium, a part is removed, the walls of the 
adjacent tubules one after another, weaken and give way 
in the direction of such withdrawal of support. In that 
case a single molecule no longer suffices for all the horizon- 
tal pressure among the separating molecules. Others 
without number now begin to enter as spheric wedges into 
the widening interspaces among the molecules, the energy 
of position is elicited, flow takes place and hydrostatics 
becomes hydraulics. 

This is the law of movement in all fluids. The flow of 
rivers, the rise and fall and march of waves, the rush of the 
storm, and all other atmospheric movements or change of 
pressure, are in their ultimate analysis molecular. Before 
a movement of flow can begin in any mass of liquid, sup- 
porting pressure must be taken away from it, and since no 
column can move until its support is withdrawn it follows 
that such support must be withdrawn column by column. 



128 



SMITH'S ESSAYS 



The Bramah Press or Hydrostatic Press 

The parts of this machine, which will best be made out 
from the drawing (Fig. 9) consist essentially of a large 
cylinder B, carrying its air-tight piston or ram P, which 
supports the table on which is placed the material to be 
compressed, A the smaller or plunger cylinder, carrying 
the air-tight piston pp, and K, the connecting pipe. 




Fig. 9. 

When pressure is made on the water in the small cylin- 
der A, it is communicated through K to the water in B. 



THE FUNCTIONS OF THE SPHERIC WEDGE 129 

When in operation the force exerted on pp, will be in- 
creased in the press as many times as the area of the end of 
the plunger is contained in that of the end of the ram. If 
P is 100 times larger than pp, then one kilo on PP will ex- 
ert a force of 100 kilos on P. 

In order to bring the operation of this machine from the 
category of the extremely complex mechanism of molecular 
spheric wedges, which it ultimately involves, into the more 
easily grasped conception of aggregated or gross wedges, 
the water in A may be regarded as unity and as laid off into 
two equal wedges with their bases in opposite directions, 
and B may be regarded as 100 times larger of area than pp, 
and laid off into wedges equal in dimensions to those in A. 
This will give one pair of wedges for A and 100 pairs for B. 
Of these, for further simpHcity, one wedge of each pair, 
either the upper or the lower, may be regarded as neutral. 

Then on driving down the plunger pp, the same quantity 
of water that is forced from A, will be w^edged off through 
K into B, and exactly suffice to advance one of the wedges 
in B with its complementary wedge, through the same dis- 
tance that the equal mass of water in A has descended. 
But instead of rising in this way, one wedge or one set of 
wedges at a time, the entering water would diffuse itself in 
equal proportions among the hundred pairs of wedges in B, 
and would cause them all to rise equally through the one- 
hundredth part of the distance descended by pp. 

Or to bring the matter still m 3re distinctly under the cat- 
egory of wedge action, and that too of the sohd wedge as 
well, let us suppose that a solid wedge having an incUne 3f 
one foot to the hundred and moving freely, is driven under 
the ram P, thus taking the place of the water from A. Ob- 



130 SMITH'S ESSAYS 

vi3usly while this wed/e is advancing one foot, the ram P 
will rise through the one-hundredth of a fo'>t : and therefore 
a driving force of one kilo on the back or base of this wedge 
will lift 100 kilos on P, but only through one one-hun- 
dredth part of the distance moved by the wedge. 

Apparently and essentially the only difference between 
the action of the solid and the liquid wedges in operating 
the press, is that while the solid wedge moves on and out, 
the liquid wedge remains coiled up under the ram. Essen- 
tially the same formulas prevail in both cases in calculat- 
ing the work done by the machine : or if reduced to the ac- 
tion of the molecular spheric wedge, and a single column 
of molecules could be forced down in the small cylinder 
pp, with the large cylinder P one inch in diameter, 
a pressure of one pound on pp would raise in P 
63,000,000,000,000,000 pounds. 

The Displacement of Fluids 

The assumption of the composite or aggregate wedge ac- 
tion will also render more simple and easily understood, the 
mechanism involved in what is denominated the displace- 
ment of fluids. 

Thus if in the illustration (Fig. 10) a cylinder C, of cork 
or any other light substance, say of one third the diameter 
of the vessel, which is partly filled with water, be let down 
into it by the cord R, it will force down the wedges A and 
B, making both of them shorter and more obtuse, while the 
wedges 1, 2, 3, 4, etc., at the sides, will become longer and 
more acute. 



THE FUNCTIONS OF THE SPHERIC WEDGE 131 

The further C descends, or rather the further it is pushed 
down, the greater the preponderance of the acute wedges 
1, 2, 3, 4, etc., over the obtuse wedges A and B, and the 
greater the tendency of C to be pushed upward. 




Fig. 10. 

Or the explanation may be based upon a still more mi- 
nute analysis of the molecular movements involved in the 
problem, and one correspondingly more subtle. Thus we 
have seen that every mass of liquid, in the last analysis, is 
composed or constituted of columns of molecules extending 
from the free surface to the bottom, balancing each other 
in pairs as in a bent tube. Now when C is pressed down 
the columns outside of C which counterbalance those be- 
neath it, are lengthened, and there then arises an increased 
tendency or stress to lift C upward on the shorter ends of 
these balancing columns. 



132 SMITH'S ESSAYS 

The Bourdon Steam Gauge 

The Bourdon Steam Gauge is an instrument consisting 
of a bent tube or hollow metal receiver, (Fig. 11), which 
straightens when steam is admitted to it under pressure, 
and which has an apparatus attached to it for registering 
the degree of straightening. 




The explanation of this straightening most commonly- 
given in the text-books, is that it is due to the pushing 
apart of the walls of the tube, which is curved on the flat. 
This is manifestly an insufficient explanation, since it is 
not at all necessary for the tube to be flattened in order to 
have it straighten under the pressure of a contained fluid. 

Professor Peddie, in his text-book on physics, recogniz- 
ing the inadequacy of this explanation, proposes the simple 
mathematical statement that the sum of the moments of 
force between C and D, is greater than it is between A and 
B. 

This proposed explanation, while entirely correct as a 
statement of fact, affords no definite or final analysis of 
the underlying principles involved in the problem. The 
conception of the fluid or spheric wedge on the other hand. 



THE FUNCTIONS OF THE SPHERIC WEDGE 133 

affords a ready and apt explanation : and in this connection 
the fiction or assumption of the aggregated spheric wedge 
presents probably its highest justification. 

The explanation on the basis of the aggregated spheric 
wedge is this : If we undertake to lay off the space in the 
receiver of a Bourdon gauge, or the space in any curved 
tube into equal segments, by making parallel sections as in 
the cut, (Fig. 12), we shall find that in order to keep pace 
with the curve of the tube, one or more wedges will have to 
be laid off in it, having their bases at the outer or long wall 
of the tube, and their apices directed to the inner and 
shorter wall. 




AC D B 

Fig. 12. 

And here again these wedges must be conceived as func- 
tioning as solid wedges, both as to interchanging mutual 
and equal support with contiguous segments or wedges, 
as already pointed out, and as having their lines pf force 
directed at right angles to their assumed plan^. 



134 



SMITH'S ESSAYS 



This being the case, it will result that every pressure im- 
pulse produced by an advance of one or more of these 
wedges, will impinge with its lines of force, first on the in- 
ner or shorter wall and then rebound from wall to wall until 
exhausted. This will be made manifest by an inspection 
of the accompanying illustration. (Fig. 13). 




Fig. 13. 



The interaction of the forces here exerted is inc!)nceiv- 
ably complex as among the molecules, and between them 
and the walls of the receiver; but the total result will be 
the same as when the resistance to the plane surfaces of all 
the wedges is divided between the inner and outer walls of 
the receiver in such a way as to give the first portion, 
amounting to one-half to the inner surface on the first re- 
bound, then half as much to the outer, then one-fourth as 
much to the inner and so on through an infinite series. In 
the final summing up of such a series, the inner wall will be 
found to have experienced two-thirds of the special stretch- 
ing force exerted and the outer wall one-third. 



THE FUNCTIONS OF THE SPHERIC WEDGE 185 

This would necessitate the greater stretching of the inner 
wall, and the consequent straightening of the tube. It is 
to be noted that the lines of force directed from the wedge 
planes, impinge obliquely upon the walls of the tube, and 
the pressure of the wedge therefore, exerts a stretching 
effect on them. 

However, in order that the receiver shall straighten, it 
is not indispensable that the inner wall shall be stretched 
absolutely more than the outer wall, but only proportion- 
ally more, and the straightening of the tube indicates that 
a proportionally greater stretching force is exerted on the 
inner wall than on the outer one. 

It may be not unreasonably questioned, however, wheth- 
er a fallacy does not possibly underlie the entire problem; 
for it might be contended with a show of reason that even 
if only the part of both walls corresponding to the bent 
portion of the curved tube should be stretched proportion- 
ally, the ends of the tube would be thrown farther apart, 
and this would be indicated on the dial. 

It hardly need be stated that in this instance as in the 
others, the action is not that of the gross or aggregated 
wedge definitely eliminated, the fiction being invoked as 
before, merely for the purposes of easier comprehension. 

The comprehension of an explanation on the basis of a 
purely molecular action is more difficult. The following 
may be offered though, it must be confessed, rather ten- 
tatively. The lines of force from a molecule functioning 
as a spheric wedge, as we have already seen, radiate in 
every direction. The closer, however, such a molecule is 
to one of the walls of the tube, the less will be the longi- 
tudinal pulling or stretching effect on that wall and the 
greater proportionally on the other wall. 



136 SMITH'S ESSAYS 

That is to say, if four radiant lines of force were project- 
ed from the center of a molecule close to the outer wall of 
a curved tube, each at an angle of forty-five degrees, two of 
them to impinge on the central line of the outside wall and 
two on the central line of the inside, those striking the in- 
ner wall would impinge more obliquely than those on the 
outer wall, and would therefore exert a greater stretching 
force. This would, of course, result in a tendency to the 
straightening of the tube. 

Relation of the Principle to Isostasy 

The principle of the fluid or spheric wedge finds apt em- 
ployment in accounting for the contour of the earth as 
well as all other cosmic bodies. As applied to the earth it 
becomes one of the most interesting features of ge jlogy. It 
is quite evident that a homogeneous liquid if not also any 
fluid mass left free in space, and unaffected by any other 
influence than the mutual attraction of its constituent par- 
ticles, will form itself into a perfect sphere. And, though 
such a body were a thousand or a million miles in diam- 
eter, its surface would not be relatively but absolutely,, 
as smooth as the rind of an orange, or even as a shot or 
a drop of water. 

However, neither of these conditions appHes strictly to 
the condition of the earth, for the earth is neither free nor 
homogeneous. But if the earth has a plastic core overlaid 
by a crust no more than thirty or forty miles in thickness, 
it exhibits departures from an even contour of surface, that 
seems hardly consistent with the principles of sphere-form- 
ing here contended for and sought to be developed. The 



THE FUNCTIONS OF THE SPHERIC WEDGE 137 

chief of these are the abysmal depths of the sea, lofty pla- 
teaus and vast mountain ranges and systems. 

If in fact there is such a plastic core of the earth within a 
reasonable distance of the surface, every considerable area 
of the earth's surface must be in a state of baric equihbrium 
or exact isostasy. Under such conditions it must result 
that every cone of equal angle, with its base at the surface 
of the earth and its apex at the center, must be of practi- 
cally identical weight with every other cone of practically 
the same construction. 

This would necessitate the conclusion that the earth 
crust of mountain areas consists of lighter material than 
the general crust; and also that beneath the ocean bottoms 
the crust must be thicker, denser and firmer than that of 
the dry land, and thickest and densest of all beneath abys- 
mal depths. These considerations must have important 
bearing on theories relating to the origin and behavior of 
earthquakes, mountains and volcanoes. 

Production and Dissipation of Waves 

The principle of the Hquid or spheric wedge is also the 
controlling element in the production, progression and dis- 
sipation of waves, both forced and free. In a free wave, 
such as may be seen following a steamer or blown up by 
the wind and continuing after the wind has subsided, or 
circling a stone that has been thrown into the water, as soon 
as it has reached its greatest height, the molecules begin to 
descend and to wedge each other apart so that the wave is 
converted into or its place is taken by a trough. The 
mass of molecules forming the crest, having the greater 



138 SMITH'S ESSAYS 

distance to fall, acquire the greater momentum and sink 
deepest into the surface of the water on which they rest: 
and thus the deepest part of the trough continuously suc- 
ceeds to the crest. The water of each passing crest be- 
comes that of the next succeeding trough. 

The action of the molecules forming the crest, is largely 
that of the solid wedge, and its effect is to divide the wave, 
forcing one part to form the advancing pha.se of the wave, 
and the other backward to form a part of the oncoming 
wave. The progress or advance of a wave doubtless de- 
pends wholly on the original impulse producing it, but it 
carries with it the mechanism of its own progression. 

The base of those wedges which are the most active and 
effective in a wave will obviously correspond with its 
crest, which in such cases is always in advance of the mid- 
dle or central point. The result is that when the wave is 
divided by the descent of its crest as a wedge, or in wedge- 
form through its body, the mass of the front portion is less 
in antero-posterior diameter than that of the aftercoming 
part. The rear portion of the wave has a longer or more 
extensive slope than that of the front part, and is more 
nearly on a level with the surface of the supporting body of 
water. The consequence is that the descending after- 
coming part continuously forces forward the newly-forming 
wave, and thus the advance of the wave is effected. 

The greatest speed of the descending crest will not be 
attained until it has passed below the line of the level of 
the general surface, and as a consequence the superficial 
portion of the wave immediately in advance of this wedge 
or this trough, in the making, will not be forced forward 
with as great speed as the deeper portions. The effect of 



THE FUNCTIONS OF THE SPHERIC WEDGE 139 

this is to produce a constant forward flow beneath the 
surface of the bottom of the trough and in advance of the 
center of the descending crest. When, however, in the pro- 
gress of a wave a shallow is encountered the retardation 
permits the surf ace water to out-travel the deeper portions. 
This reverses the direction of the under-flow of the deeper 
portions, or rather reverses the relative speed of the deep- 
er and more superficial portions, so that the relative flow 
of the under portions is backward toward the deeper 
water. Hence, the undertow of waves rushing up over a 
beach. 

The Flow of Rivers 

Reference has already been made to the contention that 
the flow of rivers is effected on the principle of the spheric 
wedge. This is to say that water flows along and out of 
the channel of a river, in the same way that it flows into a 
hole or basin made by dipping water from a vessel with a 
cup. It is not possible that the water of a whole river 
with its limited slope could slide or ghde along its cha»nnel 
as a steady mass into the sea. Throughout the last hun- 
dred and twenty miles of its course, the fall of the Missis- 
sippi River is no more than an inch and a half to the mile, 
and many other rivers have no greater fall. Now it would 
be utterly impossible for such a mass of any suubstance in 
existence, to slide down a channel of so little incline. 

The actual movement is not one of mass, but essentially 
a molecular movement. Beginning at the outlet, the 
walls of the hypothetical bent tubes previously considered, 
are weakened one after another, and their contents thus 



140 SMITH'S ESSAYS 

successively escape, and in this way a movement of flow is 
inaugurated or continued in the direction of a lower level 
ending in the level of the sea. 

Wedge Action as a Factor of Tides 

In the mechanism of the dissipation of forced waves, 
that is, of waves whose width is very great in proportion 
to their height, is probably to be found an element in 
the problem of the tides, not hitherto considered. 

A tidal mass many thousand miles in width, as meas- 
ured along lines of latitude, is drawn across the ocean by 
the attraction of the sun or moon or both, and yet on reach- 
ing the eastern coasts of the continents, this mass fades 
away, seemingly without affecting the level of the ocean to 
the eastward. This occurs every day or even three or 
four times a day, but yet each time the water on the east- 
ern continents is no higher, and that on the western coasts 
no lower than that of the previous corresponding tide. 

This mass must then, some way or somehow, each six or 
twelve or twenty -four hours, get back to the parts of the 
ocean from which it was drawn, or at least it must move to 
take the place of other water which by a wedging or 
rocking movement effects a restoration of equilibrium. 

Even if the tidal masses constantly corresponded in posi- 
tion with the poles of the ellipsoid of revolution, which ac- 
cording to the equilibrium theory of tides, the earth is 
claimed to constitute under the attracting force of the sun 
and moon respectively, the elevated mass constituting the 
tides, could be raised up only by the horizontal drawing in 
of molecules of water from without, which acting as spheric 



THE FUNCTIONS OF THE SPHERIC WEDGE 141 

wedges effect the elevation of the tidal masses. Or to 
make plainer, a cubic pound of water located directly 
beneath the moon, will probably be lightened by no more 
than the thirty-six hundredth part. Yet this water could 
not to any extent be pulled or lifted away from the earth, 
until the moon should exert upon it a differential attrac- 
tive force of more than one-hundred per cent of the attrac- 
tive force of the earth. Therefore the only influence the 
moon by its attraction can exert on such a mass directly, is 
to Ughten it, and then lift it up indirectly by driving or 
forcing other molecules under it as spheric wedges, these 
molecules having been drawn horizontally from around the 
area directly under the moon. The moon must by its at- 
traction upon the particles immediately beneath it, first 
produce an area of low pressure, and then combine T\dth the 
equilibrating forces of the earth to make compensation for 
this low pressure by producing on its site an elevation of 
the water. 

And whenever the problem of the tides shall be com- 
pletely solved and elucidated, there can be little doubt 
that this principle will be found to aid in explaining some 
of the existing inconsistences in the order of succession of 
low and high water in various situations, as well as other 
anomalous features in the phenomena of the tides. 



TIDES BY REFLUX 



INTRODUCTORY 

When the eminence and dominating personahty of the 
authorities wL have contributed to the development of the 
existing theoiie- ^ the tides are considered, it cannot well 
be otherwise thaii with the greatest hesitancy that one 
equipped with even he highest learning, could venture in- 
to the field of their di. cussion, or suggest an improvement 
in the prevailing teachings in regard to their nature and 
origin. Much more then must this be the case when such an 
attempt is to be made by one distinctly lacking in a knowl- 
edge of the higher mathematics, an attainment that has 
generally been regarded as an indispensable qualification 
for the elucidation of the problems they present. And 
though fully realizing that mathematics must have as- 
sumptions on which to build and that it does not invent or 
discover but merely verifies, the author begs to have the 
suggestion^) here offered regarded as tentative, rather 
than positive or authoritative. 

For more than two centuries the problems of the tides 
have engaged the best efforts of the master minds of science 
but their full solution has not yet been accomplished, and 
the prospect is not bright that it ever will be. 

Practically everything of substantial worth in the way 
of developing a comprehensive theory of the tides, has been 
accomphshed by probably less than half a dozen men. The 
fact is that if the contributions of Sir Isaac Newton and 
Pierre Laplace were eliminated from the discussion of the 

145 



146 INTRODUCTORY 

current theories, there would be comparatively little of 
value left. On the practical side of the subject have jBg- 
ured Bernouilli, Hough, Sir William Airy, Professor Ferrel, 
Lord Kelvin and Sir George Darwin, and these names fair- 
ly complete the list. One might conclude from the paucity 
of names connected with the problem of the tides, either 
that the earlier masters had exhausted the subject, or that 
it is too subtle for ordinary mortals. It is hoped here, 
however, to make plain that it is neither the one nor the 
other. 

And just here, in view of the fact that another and a very 
recent student of the tides, Mr. RoUin A. Harris of the U.S. 
Coast and Geodetic Survey, has become widely known, in 
fact has gained an international reputation as the expo- 
nent of a theory of tides of apparently the same essential 
character as the one here proposed by the author, and as 
there may consequently arise a question of priority, I de- 
sire to indicate with some fulness, the length of time I have 
had this theory under consideration, and the extent of 
publication given it. 

For a period of something like thirty years I have been 
cogitating a new theory of tides, or rather a supplementary 
theory, it might be called, since it adopts the major part of 
the current theories. As I now remember, I first had my 
attention definitely directed to an alternative theory of 
tides about the year 1881, while residing on the Mississippi 
near New Orleans. Finding myself unable fully to appre- 
hend the method of the production of the opposite tides, in 
the way commonly taught, I set about to ascertain if there 
might not be found a simpler and more easily comprehen- 
ded method. In the course of time there occurred to me 



INTRODUCTORY 147 

the idea, of a tide by reflux, which will be fully set out in the 
body of this essay. 

In 1884 Prof. Richard A. Proctor gave a course of lec- 
tures on astronomy in New Orleans, and while attending 
these lectures I discussed with Professor Proctor this re- 
flux theory. In the summer of 1884, while on a visit to 
Washington, the subject was taken up with Prof. Simon 
Nev>"comb and others, and later a brief correspondence was 
held with Professor Newxomb on the subject. At the In- 
dianapolis meeting of the American Association for the 
Advancement of Science, I presented a paper on the sub- 
ject, entitled, ''A New Theory of Tides," which was an- 
nounced to be read in the section on mathematics, as will 
appear from the program of the meeting of that year. 

That paper was in due course presented in the section on 
mathematics, but when submitted in the committee was 
rejected and ordered to be returned as having been offered 
in the wTong section. Prof. Charles F. Chandler of Col- 
umbia University, with a considerateness that is as fresh 
today as it was refreshing then, sought me with the rejected 
paper and returning it told me that his section was de- 
voted to pure mathematics, and that my paper was not in 
that class. He also further ad\dsed m.e to take it home 
and think over it for another year, and if I still thought it 
worthy, to bring it back and offer it again in the proper 
section, admonishing me at the same time that we should 
not conclude a thing to be true merely because we think 
it so. 

Shortly after that I contributed an article on the theory 
to the Educational Courant of Louisville and simultan- 
eously, as I now remember it, the article was published 



148 INTRODUCTORY 

in the Courier Journal. In 1899 I published a book, 
"The Philosophy of Memory and other Essays," for 
which I had prepared an article on "'Tides by Reflux." 
Just about that time Sir George Darwin's great work on 
tides appeared, in which he still adhered to the old theory. 
Fearing that it might be that I was self-deluded, and re- 
membering Professor Chandler's advice, I withdrew the 
article after it had already been placed in the hands of 
the printer. Mention is made of this fact in the introduc- 
tory, on page 99 of "The Philosophy of Memory," and 
two pages 120 and 121 of that work, at the end of the arti- 
cle entitled " The Functions of the Fluid Wedge, " are given 
to the theory. 

I do not remember having had up to this time any inti- 
mation that any one else had ever thought along the same 
line. Later, however, I learned that Mr. RoUin A. Harris 
of the U. S. Coast and Geodetic Survey, had in 1907 con- 
tributed articles to the U. S. Weather Review, on a theory 
of tides based on rocking or oscillating movements of ex- 
tensive masses of water in the ocean basins, due to the 
successive attraction of the sun and moon. These rock- 
ings or oscillations were supposed to be worked into har- 
mony by the rotation of the earth, in accordance with a 
great law of physics developed by Laplace. Still later I 
had opportunity to read the article on tides in the Ency- 
clopedia Americana published in 1903, which was written 
by Mr. Harris and in which he had set forth similar views. 

The theory as advocated by Mr. Harris has received 
notable attention in the New Encyclopedia Britannica at 
the hands of Sir George Darwin, and it seems to have won 
a growing recognition in high scientific quarters. I have 



INTRODUCTORY 149 

no evidence nor good reason for believing that Mr. Hams 
ever saw my published views on the subject or heard of 
them, but I have thought it only justice to myself to enter 
into the matter at this length, to show that I have at least 
not plagiarized nor sought to appropriate laurels won by 
another, in setting forth this theory. 



TIDES BY REFLUX 

The word tide is used primarily to indicate the periodic 
rising and falling of oceans and other large bodies of 
water, due primarily to the attraction of the moon and 
sun. 

The phenomena of the Tides must have been a subject 
of consideration and interest long before the beginning of 
history. In historic times, the Greeks and Romans 
discussed the subject extensively. But not till the time 
of Sir Isaac Newton was any serious and systematic 
attempt made, so far as known, to ascertain cause of 
tides and the laws by which they are governed. 

Newton's Theory 

The solution of the problem of the tides, offered by Sir 
Isaac Newton, called the static or equilibrium theory, 
is based on the unequal attraction of the sun and moon 
respectively, as exerted on different parts of the mass of 
the earth including the waters that cover it. For the sake 
of simplicity, we will consider only the tides produced 
by the moon, the principle in those produced by the sun 
and moon being identical. The tides under or nearest 
the moon and sun we will for convenience of description 
call proximal and those opposite, we will call distal. 

The moon by its attraction draws upon the part of the 

151 



152 SMITH'S ESSAYS 

earth next to it more strongly than upon the remoter 
parts successively and least strongly upon the part most 
remote from it. Since the solid core of the earth is a 
continuous mass, the moon can draw toward itself the 
water upon the part of the earth nearest it, but cannot 
pull the parts of the earth nearest from the parts more 
remote. But the water surrounding the zenith point on 
the earth's surface can be pulled obliquely away, to some 
extent, from the waters farther away that flood the soKd 
earth. The water thus drawn toward the moon can, 
therefore, be heaped up into an elevation on the side of 
the earth nearest the moon. 

The Distal Tide 

But there is also, or is supposed to be, a tide on that 
part of the earth most remote from the moon. How is 
that produced? The part of the earth, as already said, 
nearest the moon is attracted most by it, and every layer 
more remote is attracted in a less degree, until the last 
layer is reached and this is attracted least of all. The 
result of this is that the solid mass of the earth must as 
one continuous body follow the part nearest to the moon 
and move as one toward the moon; but the water of the 
far side, being able to separate from the nearer waters, is 
left behind by the solid earth and is thus heaped up into a 
tide on the opposite side of the earth. Since the earth 
revolves on its axis every twenty-four hours, the result of 
these conditions will be that there should be two tidal 
elevations every twenty-four hours at any given point on 
the earth's surface. But as the moon revolves in the 



TIDES BY REFLUX 153 

same direction as that in which the earth rotates, it gains 
on the earth about fifty minutes each day so that there 
appear at any given station two tides every 24.50' 28''. 

Newton demonstrated all this with a clearness and 
conclusiveness that is characteristic of the work of the 
great mathematicians; but it was found that the tides 
failed quite uniformly to appear just at the place his 
mathematics prescribed for them. The fact is that in- 
stead of keeping up with the moon, the tides follow at 
quite a distance behind it, frequently just about as far 
behind it as they well can. Often the tides lag as much 
as six hours behind the moon; and they could not do 
more, for then they would be nearer the next tidal moon 
or meridian, which is twelve hours away. This lagging, 
Newton attributed to the viscosity of the water, and he 
strove to reconcile it with his theory by the employment 
of additional mathematics. Thus buttressed, for about a 
century and a half no man ventured to question Newton's 
Theory. 

LaPlace's Forced Wave Idea 
OR The Dynamic Theory 

At length there appeared on the scene another mathemat- 
ical prodigy, the great Frenchman, Laplace. This 
philosopher took notice of an important fact known to, 
but not considered by Newton, namely: that the tides to 
keep pace with the moon, must when near the equator, 
travel at a speed of 1,000 miles an hour, and that such 
speed can be attained by a free wave only where the water 



154 SMITH'S ESSAYS 

has a depth of 13% miles. Since the ocean is very rarely 
as much as jfive miles in depth, it is clearly impossible for 
the tide, as a free wave, to keep . pace with the moon 
around the earth. 

Laplace then substituted the idea of the forced wave 
for the free wave. But this too, though it met the re- 
quirements of speed did not explain the observed anoma- 
lies and irregularities; the tides still did not appear where 
the calculations placed them. Laplace, therefore, as an 
aid in his calculations contrived the fiction of a succes- 
sion of satellites as co-operating in the producti3n of the 
tides; and this proved distinctly helpful, for if the tide 
could not be made to go to the moon, one of these moons 
could at least go to the tides. Furthermore, this fiction 
probably suggested the invention of a machine that pre- 
dicts the times and quality of the tides with wonderful 
accuracy. And here again the development of the prob- 
lem in its theoretic aspects, rested for mother century. 

Tides by Oscillation 

Quite recently there has come into notice a new and 
in many respects, a rival theory of tides, whose best known 
exponent is Mr. Rollin A. Harris, already referred to in 
the introductory. 

The theory of Mr. Harris bases the tides upon the suc- 
cessive action of the tidal forces upon oscillating systems, 
each having as free periods, approximately the period of 
the forces, and each perfect enough to preserve the general 
character of its motion during several such periods, were 
the forces to cease their action. 



TIDES BY REFLUX 155 

The law which is supposed to govern these oscillations, 
and which was enunciated by Laplace, is as follows. 
"The state of any system of bodies in which the primitive 
conditions of motion have disappeared through the 
resistance which the motion encounters is co-periodic 
with the forces acting on the system. " This law may yet 
be found to apply to a wide field of oscillations or vibra- 
tions, for it is not certain that the vibration of atoms 
that constitutes light are not compounds of the vibrations 
of the ions or electrons that so far as known are the ulti- 
mate elements of matter. 

Theory of Tides by Reflux 

The foregoing theory of tides by oscillation or rocking 
movements propounded by Mr. Harris, and that of tides 
by reflux suggested by the author will, it is believed, be 
found on careful examination to be substantially the same 
except that the theory of reflux appears to be more com- 
prehensive. But while maintaining claim to its prior sug- 
gestion, it is frankly confessed, that the admirable mathe- 
matical development of the principle accomplished by 
Mr. Harris is quite beyond the attainments of the author. 

The theory of tides by reflux may be stated as follows : 
Let us regard the earth and moon as being fixed relatively 
to each other; that is, held apart as if by a rod or pole. A 
tidal elevation and the only one on the earth, would be 
raised about that end of the rod which rested against the 
earth. Now suppose that after the fullest tide is raised 
beneath it, the moon is instantaneously obliterated and 
passes out of existence. Clearly the waters of the tidal 



156 SMITH'S ESSAYS 

elevation will then fall away and by reflux meet and 
gather on the opposite side of the earth, as happened 
three times successively with the atmosphere after the 
cataclysmal explosion of Krakatoa. In such a case we 
should have an opposite or distal tide, and thus the two 
tidal elevations required to meet the existing conditions. 

Now the moon, in the actual case, is of course never 
wholly obliterated; but after the tide has been raised by 
the moon's attraction, the moon runs away from it at the 
rate of 1,000 miles an hour, and is to this extent obliterated 
thereby as to each tidal elevation. The tidal elevations 
thus abandoned, fall back and form again on the opposite 
side of the earth. 

But this leaves the same difficulty in regard to the 
position of the tide relative to that of the sun or moon, 
as do the theories of Newton and Laplace; for the tides 
are neither the one nor the other directly under or opposite 
either the moon or the sun. How is this to be accounted for ? 

It is to be accounted for in this way. Immediately 
beneath the moon there can be no tidal elevation directly 
produced by its attraction. A vessel of water, for illus- 
tration, set on a sand bar at sea level, cannot be directly 
lifted up by the moon's attraction even in the smallest 
degree. Nor any more can the same or any other quantity 
of water remaining in and constituting a part of the sea 
be so lifted up by the moon in a direct manner. 

If a portion of the water of the ocean could be raised 
up directly to the extent of the millionth part of an inch, 
it could be raised through the next millionth still more 
easily, for it would be by so much farther from the 
earth's center and so much nearer the center of the 



TIDES BY REFLUX 157 

moon, and it would be eventually drawn quite to the moon. 
Other water would take its place, to be drawn to the 
moon in turn, and eventually all the ocean would be 
emptied on to the moon's surface. 

It would follow then that the water of the ocean can 
only be drawn in obliquely from the area surrounding the 
portion of sea immediately beneath the moon, and thus 
by a double inclined plane or wedge action, heaped up 
under it. 

Tide Mass a Circle 

If now, after the subsidence of all the proximal tide 
mass, our vanished moon were to reappear all at once at 
the end of its pole, a ring of tidal elevation would arise 
from the sea extending all around its zenith point. But 
in the area embraced in this ring the water would remain 
low and practically unaffected except to the extent of 
a shght lightening, until the water of the elevated ring 
should move in and raise it by wedge action or a process 
of equilibrium. The production of this elevated ring or 
ridge is due in part to the unequal attraction at different 
distances from the moon, in part to the obliquity of the 
moon's pull and in part to the great length of the line of 
the molecules of water through which the lines or rays of 
attraction must pass when they barely miss the solid core 
of the earth. 

If a cord could be stretched straight from the 
center of the moon so as just to miss the solid core of the 
earth and then onward, it would pass for about 400 miles 
through the water of the sea, provided the sea was as 



158 SMITH'S ESSAYS 

much as five miles deep. But if a like cord should be 
extended from the center of the moon to the nearest 
point of the soUd core of the earth, and by the most di- 
rect way,it could pass no farther through the water than the 
actual depth of the sea, say six miles at the most. 

The lines of the moon's attraction would have the same 
experience as the cord, and would have eighty times 
greater distance to pass through water and eighty times 
more molecules of water to draw upon in a consecutive 
way, than would the lines directed to the nearest point 
of the earth's solid core. This oblique inward pull on the 
water aided by wedge action would serve to elevate the 
water in the middle also, if sufficient time were given it. 

Why Not a Forward Tide? 

"But, " it may be asked, "if it be true that a tide is all 
the time being raised up in the form of a ring extending 
quite around the low area under the moon or the sun, 
why is it that we see a tide only following the moon and 
sun.? Why is it that there is not a tidal elevation moving in 
advance of the moon as well as following it, seeing that 
the moon draws with equal force upon the water in ad- 
vance of it and that behind it? 

The reason is simply this : We have seen that the moon 
cannot lift the water immediately beneath it. It draws 
obliquely on the water in advance of itself as well as on 
that behind it, and with like force; but before the water in 
advance of it can be raised up into a tide, the moon, 
traveling 1,000 miles an hour moves forward over this 
inchoate tide and holds it down; that is, the moon when 



TIDES BY REFLUX 159 

directly over a point can neither lift or directly raise up 
a tidal mass, nor hold one up though already lifted; 
unless the middle is supported by water already drawn in 
from around. 

Therefore the water drawn in toward the moon in front, 
but not lifted, and that drawn up after it and lifted into 
a tidal elevation, is by the partial obliteration of the moon, 
due to its running away at the rate of 1,000 miles an hour, 
allowed to settle back along the shortest lines so as to meet 
and form a tide on the opposite side of the earth. In the 
ocean basins this necessarily results in a process of rocking 
or oscillation, and that aspect of the tides so effectually 
developed by Mr. Harris as previously mentioned. 

It may be perceived at a glance that both the sun and 
the moon exert just as much tide-raising power in advance 
of themselves as in their rear, even though it be not shown 
by an elevation. Therefore when the moon changes 
position, or the sun, so as to alter the direction of such 
force, the force expends itself as a reflux in producing the 
opposite or distal tides. 

Of course, in the actual case the problem is not so simple 
as I have tried to make it here, for there are many features 
of this almost infinitely involved and intricate question 
that are as yet unexplained and that bid for a long time 
to remain so. 

The Mechanism of the Distal Tides 

Let us now investigate the intimate nature and mechan- 
ism of the distal or remote tides; and for simplicity we 
may still take those due to the moon. 



160 SMITH'S ESSAYS 

The causes assigned for the origin of the distal tides 
may be divided mainly into three. The jBrst is the partial 
withdrawal of the moon's attraction from the remoter 
part of the earth, and especially from the water covering 
that part of the earth. 

The second is the centrifugal force exerted on the re- 
mote waters while the earth is revolving around the com- 
mon center of the earth and the moon. This centrifugal 
force is supposed to be made effective in the production 
of tides by reason of the fact that the solid core of the 
earth is adherent to the part near the moon, which is the 
most attracted by the moon, and cannot be withdrawn 
from it, while the remote waters being free to move are 
thrown out by this tangential or centrifugal force to form 
the tidal elevation. 

The third is the reflux of the water which has been 
raised by the sun and moon on the side of the earth, next 
to them and then left by a partial obliteration of the 
attraction of these bodies due to the earth's rotation to 
fall back and form a tidal elevation on the opposite side 
of the earth. 

Distal Tides and Unequal Attraction 

The production of the distal tide by the unequal attrac- 
tion of the sun and the moon on the nearer and more 
remote parts of the earth seems to be the one mainly 
relied upon by Newton. We will now examine the mechan- 
ism of this supposed method of production. 

In discussing the proximal tides it was shown, that the 
sun and moon draw strongest on the part of the earth 



TIDES BY REFLUX 161 

nearest to them, less strongly for every filament or 
lamina of the earth farther away, and least strongly upon 
the parts most remote, that the earth being a solid 
adherent mass, could not be pulled apart, and that there- 
fore the remote parts of the solid core must follow the 
nearer parts toward the moon; with the result of pulling 
the solid core away from the remote water, thus leav- 
ing the water behind as a tidal elevation. 

Let us now attempt to realize the definite steps by 
which this elevation would need to be brought about 
under the static theory in whose interest the explanation 
is offered. 

In the first place there could be no elevation of the 
water produced in this way at the nadir points of either 
the sun or the moon. As in the case of the proximal 
tides already considered, a large circular area opposite the 
moon as well as the sun must for a time remain low. 
Water is non-compressible under pressure and would not 
expand by reason of its removal. To rise then it must 
either be wedged up from around, or it must be lifted free 
from the earth, leaving a cavern beneath it. 

If water unassisted and unpropelled except by the 
earth's attraction flows in to produce this elevation it 
must move in only with the speed of water moving under 
the ordinary forces of equilibrium, and probably move 
little faster than a rapid river or the Gulf stream. But 
if made lighter and heaped up, what then? The lighter 
water would flow away at the surface just as heated air 
flows away above when it rises over a considerable area; 
just as the Gulf stream flows away from the Equator. 
But the earth attracts this distal water, in round numbers 



162 SMITH'S ESSAYS 

thirty-seven hundred times more strongly than the moon, 
and the mo3n attracts the near water by a force one- 
thirty-four hundredth time that of the earth. That is, 
the moon attracts the remote water by a force one fifty- 
four thousandth part of the amount of the earth's attrac- 
tion less than it attracts the near water. 

The earth therefore attracts a particle on its distal 
surface thirty-seven hundred times more strongly than 
the moon does. But all of the moon's attraction except 
the quantity lost in traversing the diameter of the earth, 
which is equal to one fifty-four thousandth of the earth's 
attraction, is exerted through the earth upon the distal 
water and pulls it against the earth and thus makes it by 
so much the heavier. It seems then dilBBcult to conceive, 
merely upon the ground of the moon's unequal attraction 
for the two sides of the earth, how the opposite or distal 
tide could be raised, even though the earth and moon 
stood still relatively to each other. 

Revolution About Common Center 

The second cause ascribed for the production of the 
distal tides is the revolution of the earth about the com- 
mon center of gravity of the earth and moon; and this 
whether it operates to a greater or smaller extent must 
be a vera causa as far as it goes. 

This common center is 1,000 miles beneath the surface 
of the earth and on the same side as the moon. Every 
fourteen days the moon pulls the earth 1,000 miles out of 
its normal path around the sun. This is at the rate of 
three feet per second. But the earth pulls a body to itself 



TIDES BY REFLUX 163 

at the rate of sixteen feet per second. It would therefore 
be impossible for the moon by means of the centrifugal 
force exerted by it to lift up the distal water. But it might 
move the water found at some distance away from the 
remote central point, horizontally toward that point, and 
by means of the spheric wedge action of the invading 
water elevate to a slight extent the low area. 

But could there be enough centrifugal force developed 
by the means in question, to produce a tide of the magni- 
tude of the observed distal tide; and especially when it is 
considered that this tide is almost never found at the 
farthest point and is often found as much as six thousand 
miles away from it.'^ 

Distal Tide by Reflux 

It has been shown that the moon must tend to produce 
its tidal elevation in the form of a ring occupying the 
circle on which those rays of attraction that just miss the 
solid core of the earth enter the water of the ocean, and that 
the portion of the circle in front is not permitted to rise 
because the moon advances over it before it has time to 
rise. This then leaves the main tidal elevation, often 
many thousand miles in the rear of the moon, to move 
by reflux to that part of the ocean antipodal to it. 

Of course, no single particle of water moves any con- 
siderable distance. The equilibrium of all the water is 
disturbed, and the reflux or return of the water to its 
proper position is like the rising of a field of wheat bent 
by a passing wind and then released. 



164 SMITH'S ESSAYS 

Tides at the Poles 

The existence of tides at or near the poles favors the 
reflux theory rather than the others. Why should there 
be any tide in the polar regions if produced in accordance 
with the current theories? According to accepted theories 
there ought to be all around the chief points of tidal eleva- 
tion, and at a distance from them of one-fourth of the 
earth's circumference, a belt of low water which would 
always embrace the poles. 

By reflux only does it seem possible that we should 
have tides in the polar regions. If the poles were land- 
capped, then the shores of that land might experience 
strong tides if they were produced by reflux. But if the 
polar regions were occupied by deep water and covered 
with heavy ice, then the tides there should be small, or 
little more than potential, for the ice-caps would rest 
more heavily on the crest of the wave than on the 
trough, and would thus hinder or destroy the manifest- 
ation of the tidal force. 

Tide-Raising Power of Sun 

The history of tides due to the moon may be applied to 
those of the sun as well, except in the particular that the 
tides raised by the moon are much larger than those 
raised by the sun. 

The sun pulls the earth with a force 25,500,000 times as 
great as that of the moon and yet the tides raised by the 
sun are, according to the calculations of all the astronomers, 
just YoQ ^^ great as those produced by the moon. 



TIDES BY REFLUX 165 

Newton made the calculation that gives this result on 
the assumption that gravitation is inversely as the square 
of the distance between two attracting bodies, while the 
tide-raising power is inversely as the cube; and all the 
world has accepted that assumption and conclusion up 
to this good hour. 

Let us endeavor to elucidate a little more clearly and 
fully this proposition that the tide-raising power of an 
attracting body is inversely as the cube, while gravity is 
inversely as the square. With this aim let us consider 
the parallel case of the expansion of a beam of light. We 
may imagine the beam of a searchlight starting out from 
the center of the moon toward the earth, and of such 
dimensions as just to cover the disc of the earth on reach- 
ing it. Such a beam would have a length of 240,000 miles, 
and a diameter at its larger extremity of 8,000 miles. 
Now let us imagine a similar searchlight-beam starting 
from the center of the sun, and likewise of such dimensions 
as just to cover the disc of the earth on reaching it. This 
beam would have a length 400 times greater than the 
other, but at a distance of 240,000 miles from the sun; — 
the distance of the moon from the earth, — it would meas- 
ure less than twenty miles in diameter, against 8,000 
miles in the case of the moon, at the same distance from 
the starting point. The lines of the sun's attraction would 
here be nearly parallel. 

Or another illustration may make it even plainer. 
Suppose a load of shot to be fired at a paper target one 
foot in diameter, frjm a point twelve feet distant, and 
that sixty-foiu- shot pierce this target. Another target 
likewise one foot in diameter and twelve feet further on. 



166 SMITH'S ESSAYS 

would receive only sixteen of the shot piercing the first 
target. But if a target one foot square, at a distance of 
seventy-two feet should be pierced by sixty-four shot, 
then a second target one foot square, in line with this, and 
also twelve feet further on, would receive fifty shot. It 
is this differential between the near and long distance 
shots that represents the tide-raising power of an attract- 
ing body through gravitation, and which is involved in 
the proposition that gravity is inversely as the square, 
and the tide-raising power is inversely as the cube of the 
distance between two bodies. 

Attraction by the sun proceeding along lines that pass 
through the water of the ocean so as just to miss the solid 
core of the earth, being less oblique than those of the 
moon, would enter the water in a larger circle, and raise 
a tidal ring of larger diameter than that of the moon. 
The area of low water embraced in the ring would be 
larger and the elevation less, and the tides being lower to 
begin with, and having a shorter distance to travel, would 
in their reflux, produce a smaller tide on the opposite side 
of the earth than would those of the moon. 

The accepted theories as already indicated give to the 
sun a tidal force just a little less than half that of the 
moon, yet inspection of the tide tables readily shows that 
the tides due to the sun are rarely twenty per cent and 
oftener not more than five or ten per cent as high as those 
of the moon. This is against both the static and dy- 
namic theories and favors the theory of reflux. 

Mechanism of Reflux 
But as to the water that is raised into the visible tide 



TIDES BY REFLUX 167 

following the sun md moon, gnd in regard to which they 
at each step suffer partial obliteration, can it be dissipated 
or disappear by flowing or moving away in all horizontal 
directions, or must it flow or settle backwards only, and 
not forward imder the moon and sun? 

We must, it seems, assume that it can move forward as 
well as backward, as it ccitainly must move toward the 
poles both north and south, that is, that adjustments of 
equilibrium can take place in all directions. It is certain 
that the flood that each day runs in upon the coasts of 
the continents, and the great tidal floods that move out of 
the deep southern oceans to the northward, must, when 
they have spent their force, move back to their position 
of normal equilibrium by a kind of far-re iching rock- 
ing or balancing movement effected through the medium 
or instrumentality of counterbalancing molecular columns, 
and of molecules functioning as spheric wedges. This 
part of the problem, however, has been treated as fully 
as space would permit in *'The Functions of the Spheric 
Wedge," another essay of this series, and to that the read- 
er must be referred for a fuller exposition of the principles 
involved in the problem of readjustment. 



CYCLONES, COLD WAVES. AND TORNADOES 



INTRODUCTORY 

For some twenty years past the author has been con- 
tributing to various pubhcations, articles contending for 
the view that cyclones, hurricanes and typhoons originate 
over tropical islands. From time to time ideas that 
are seeming discoveries, relating to other features of these 
atmospheric disturbances have occurred to him, the 
principal of which are the source of their energy and 
the mechanism of their progression. Articles on this sub- 
ject, contributed by him, have been published in Science, 
the U. S. Weather Review and Symon's Meteorological Re- 
view of London. 

The author's conclusions on the subject are here pre- 
sented at length for the consideration of such students 
as may deem themselves qualified to pass on their merits, 
in full confidence that they will bear investigation. 



171 



CYCLONES, COLD WAVES, AND TORNADOES 

Of all the influences that render the countries of the 
temperate zones a desirable home for humanity, no other 
factor, perhaps equals that of the cyclone. 

Without its beneficent contributions to the climate of 
these regions, the whole of eastern North America, and 
much of eastern Europe, would be little better than 
a desert waste. A drizzle of rain, that in the summer at 
least, would dry almost as fast as it fell, and light and 1 )ng 
continued snowfall equally as diffused, would constitute 
almost the only source of moisture. Throughout the 
summer season the wind would be almost constant during 
the day, while at night and during the winter, there would 
persist a stillness of the atmosphere, approaching a con- 
tinuous calm. Agriculture would be well nigh prohibited, 
and a scant pasturage would be almost the only source of 
supply for human food. 

Tropical regions on the other hand, would suffer with 
interminable rains. The water that evaporates from the 
ocean must somewhere fall, and in the absence of any 
contrivance for drawdng the moisture-laden air from 
equatorial regions toward the poles, the over-saturated 
atmosphere must in tropical and subtropical regions, be 
constantly pouring out its moisture. 

It is easy to perceive, then, that there are few if any 
features of climate in which mankind can have a deeper 

173 



174 SMITH'S ESSAYS 

concern than in the extensive circular and ascending 
movements of the atmosphere, variously termed, in 
diflferent lands, hurricanes, typhoons and cyclones. 

These great aerial disturbances bring the principal part 
of useful rains and snows in temperate regions, they modify 
climate in a most agreeable and healthful way, while at 
the same time they often carry messages of terror and 
work appalling destruction. 

These gyrating masses of atmosphere vary in diameter 
from 20 to 2,000 miles or more, they are constantly ap- 
pearing over the greater part of the earth's surface, they 
usually travel for great distances before disappearing, in 
many instances possibly making the circuit of the entire 
earth: and yet, though they have been long and deeply 
studied, they still present many striking features not 
hitherto explained. 

The unexplained features embrace among other things, 
the origin of cyclones, the source of their energy and the 
mechanism of the application of that energy in eflfecting 
their rotation and progression. Beside these matters 
relating to cyclones, there remains not a little yet to be 
revealed in regard to the origin of cold waves and torna- 
does, which are probably in the large majority of cases, 
the oflf spring of cyclones. 

We may pass by a consideration of the principles imder- 
lying the basis of atmospheric movements, embraced in 
the philosophy of fluid equiHbrium, as that subject may be 
found discussed at length in another essay of this volume. 
We cannot, however, prudently forego a brief explanation 
of the cause of the gyratory movement of cyclones, since 
without a knowledge of this subject, the reader would be 



CYCLONES, COLD WAVES AND TORNADOES 175 

deprived of much of the zest otherwise afforded by their 
study. 

Why Cyclones Rotate 

If a man were standing on the equator the rotation of 
the earth would be carrying him to the eastward at the 
rate of a Kttle more than 1,000 miles per hour. If he 
could then spring up all at once to the height of the clouds, 
he would continue to mo\'e to the east at the same rate, 
always assuming that the atmosphere offered no resistance, 
and that he would remain over the same spot on the 
earth's surface. Let him now start directly toward the 
north pole. When he reaches the 65th degree of north 
latitude, he will still be traveling to the eastward at the 
rate of 1,000 miles an hour, while the earth beneath him 
will be moving eastward at the rate of only 500 miles an 
hour. 

Suppose now that another man starts from the pole 
toward the equator and on a line continuous with that 
traveled by the first. At the 65th degree of north latitude 
he finds that he is moving to the westward at the rate of 
500 miles to the hour, or that the surface of the earth is 
moving under him toward the east at that rate. Say 
that at this point he strikes plump against his fellow 
traveler. Clearly since the traveler from the north is 
moving westwardly and the one from the south is moving 
eastwardly, when they meet, if locked in each other's 
arms, they will begin to whirl around each other in a 
direction denominated "against the sun" and also "con- 
tra-clockwise. " 



176 SMITH'S ESSAYS 

If the two men were replaced by two masses of air, no 
matter from what direction they came, these two masses 
would begin to whirl in the same manner. It is obvious 
then that if the air should begin rising at any spot, and 
other air should rush in from around to take its place, 
the inrushing air would rotate in mass, contra-clock-wise, 
and would continue to do so as long as it was fed from 
around. 

This brings us to the immediate discussion of the move- 
inents of a cyclone, and in order to render the discussion 
of the subject simpler and easier, we may find distinct 
advantage in the expedient of attempting to weave into 
the life history of one of these great disturbances, the 
incidents that are supposed or known to accompany it 
throughout its career. 

For this purpose let us take one of the cyclones coming 
into the United States by way of the West Indies, and 
known while there as a hurricane. 

Origin of Cyclones 

When we consider, as already mentioned, that a cyclone 
may and frequently does attain to the diameter of 2,000 
miles or more, that it has the might of nearly half a million 
horse-power, so that if every third human being on the 
face of the earth were to lead up a dray horse to be har- 
nessed into its work, the vast equine concourse would 
scarcely suffice for the requirements of its movements: 
and again when we consider the interest cyclones possess 
for humanity, the terror they sometimes spread in their 
advance, and the blessings they may leave in their wake. 



CYCLONES, COLD WAVES, AND TORNADOES 177 

there intrudes a feature not the least strange of all, namely : 
that the place and manner of their origin, are still un- 
known or much-disputed facts. 

It has sometimes been rather loosely claimed that 
hurricanes have been known to spring up among the 
islands of the West Indies, but it is doubtful if there is to 
be found an authenticated record of a single West Indian 
hurricane, that might not have been traced back to sea 
eastward of the Windward Islands. However, if any 
number of them should be proved to have arisen over the 
small islands bordering the Carribean Sea, it would not in 
the least militate against the theory of their origin about 
to be presented. This theory would place their origin in 
the ascending currents of heated air over tropical islands. 

Wherever the heat of the sun renders the air over the 
land hotter than that over an adjacent sea, the air of the 
land rises up and that over the sea flows in to take its 
place. When such land area is an island, the inflowing 
air as it moves in and upward must take on a spiral motion. 
It thus happens that the atmosphere over every island 
of the globe that has a sea breeze, must every day while 
such a breeze is experienced, rise up as a gyrating mass 
that differs in no essential feature from the mass forming 
the body of a cyclone. Even a burning house or brush-pile 
produces such a movement. 

In the vast majority of cases, as night comes on, the sea 
breeze lulls, the island cools, and the incipient cyclone, 
typhoon or hurricane is dissipated. But now and then, 
say over one of the Cape Verde islands on the east coast 
of Africa, a favoring condition of the winds intervenes, 
and the cyclone starts away to the westward on its long 
and eventful journey. 



178 SMITH'S ESSAYS 

Let us now inquire for a moment what these favoring 
conditions may be. First, there is the overhead westerly, 
or westwardly blowing, equatorial air current. The 
trade winds of the region are coming in from the north- 
ward and as they approach the equator they are veering 
to the westward. When they have reached a line within 
a few degrees of the zenith point of the sun they begin 
to rise up curving first poleward and then eastward, to 
become the constant overcurrent as they gradually ap- 
proach the polar regions. 

The trade-winds when they have reached their nearest 
point of approach to the equator, on the surface, do not, 
however, rise up perpendicularly but with a curve, so 
that on their equatorial border the trade-winds are still 
arching overhead and veering to the west, long after they 
have ceased on the surface of the earth beneath, or have 
risen up from it. 

This westward-rising movement of the trades sets the 
whole body of the upper atmosphere over the region of 
the equator into a constant movement to the westward at 
the rate of some 70 miles per hour. 

Locality of Origin 

Having briefly considered the conditions under which 
cyclones are supposed to originate, we may now pass to a 
more extensive examination of the question of the prob- 
able locality of their origin, though it is not easy to con- 
sider one of these questions without connecting it more or 
less with the others. 

In all the literature of cyclones, even the very latest. 



CYCLONES, COLD WAVES, AND TORNADOES 179 

one looks in vain for an authentic account or a clear-cut, 
definite history of the origin of a cyclone. The report of 
observations made by seamen in the Bay of Bengal, show 
them to have come nearer being present at the birth 
of a cyclone or typhoon, than any other observers who 
have put their experiences to record. 

It is to be borne in mind that not all so-called "lows" 
are cyclones. The weather maps oi the day are dotted 
with indices of depressions more or less circular, which are 
not true cyclones, and which are filled up by the ordinary 
processes of equilibrium. These depressions may prob- 
ably be produced in many ways, chief among which is 
most likely the momentum of masses of air moving by 
each other in different or diverging directions. The 
momentum of such masses pulling them apart, would 
naturally result in the production of "lows" ci greater 
or less extent. A true cyclone must be a whirling body 
throwing out a stream of air at its summit, and conse- 
quently drawing in the air at its base. 

Now it is known that nearly all the disturbances called 
hurricanes and typhoons in the tropics, when in their 
ellipsoid or hyperbolic paths, they have curved to the 
poleward and begun to travel to the eastward, become 
typical cyclones of the temperate zones. And with the 
exception of a small number that in the tropics continue 
their course westward and are lost in the equatorial belt, 
this is the course they mostly pursue. As for the cyclones 
of temperate America, it is a question yet to-be determined 
whether or not they are theoutcome of typhoons, which have 
arisen in the neighborhood of Japan, the Ladrones, the 
Caroline Islands, and the Philippines, and are continuing 



180 SMITH'S ESSAYS 

their journey to the eastward. With great uniformity, 
the majority of the cyclones that traverse the United 
States are jBrst observed coming in from the Pacific. 

In the West Indies hurricanes can be traced with great 
uniformity to a probable origin in the region of the Cape 
Verde Islands, and invariably to an origin as far east as 
the Windward Isles. The comparatively small number 
of cyclones disturbing the west coast of South America, 
may be explained by the small number of islands, found 
on the coast of that continent. The Pacific Ocean is 
pacific and received its name as such, probably because 
there are few islands off the western coast of tropical 
America to give rise to cyclones. 

The seasons at which the greater number of West 
Indian hurricanes occur, favor the view that these hurri- 
canes arise over the Cape Verde Islands: for as the dol- 
drums recede to the south and expose these islands to 
the influence of the trades, hurricanes begin to appear 
less abundantly. 

One could not confidently or safely affirm that true 
cyclones arise in no other way than as here suggested, 
that is to say, out of the ascending atmosphere of tropical 
islands, but in view of all the facts it may be reasonably 
contended that the probabilities point most strongly to. 
such a conclusion. 

SOUKCES OF THE EnERGY OF CyCLONES 

The cyclone, then, having probably arisen in the way 
suggested and starting on its journey to the westward, is 
supplied with motive power partly by the westwardly 



CYCLONES, COLD WAVES, AND TORNADOES 181 

flow of the trade-winds, partly by the precipitation of its 
vapor changed into rain, thus releasing heat for the heat- 
ing and expansion of the air constituting its mass; partly 
by the relief given by the precipitation of its vast burden 
of water; but perhaps most of all by the action of the 
overhead westerly equatorial winds, and later the anti- 
trades and the constant easterlies. 

Westerly Flow of Trade-winds. The trade-winds by 
their westerly flow and coincident rising, exert a double 
influence. In the first place, since the cyclone under the 
circumstances, moves along the line separating the trade- 
winds and the doldrums, it incorporates into itself largely 
of the rising and westerly trades, and thus appropriates the 
force derived from their momentum, both in the upward 
movement of its constituent elements, and in the for- 
ward movement of the mass. The overhead trades or 
antitrades, which by a curved path, convex to the west 
and south, are returning north, also tend all along their 
course to pull the cyclone to the northward; and later 
when these winds have become the constant easterly 
ciu'rent, they carry the cyclone on its final journey to 
the east. This feature will come up for further considera- 
tion later on. 

Energy from Precipitation, The power supplied by the 
heat due to the condensation of the vapor in the mass of 
the cyclone, as well as that derived from the lightening 
of the cyclone mass due to the unloading of its moisture 
in the form of rain, will be directed upward and expended 
mainly in the gyratory movement. Great importance 
has been, and still is, given to the influence exerted by 
the heat released by the condensation of the vapor of 



182 SMITH'S ESSAYS 

cyclones and the resulting expansion, but in the author's 
opinion this factor is greatly overrated. 

Mere expansion of air does not create an area of low 
pressure. The air must not only expand in order to create 
an area of low pressure but it must expand and flow away. 
If the atmosphere in a cyclone expands from any cause, 
the first effect is to raise the barometer underneath in the 
process of overcoming the inertia of the air super-imposed 
on it, just as the first effect of building a fire in a tall 
chimney is to force the smoke out below. It is only when 
the air in a cyclone or any other area is expanded and has 
time to overflow and leave an area occupied with the 
lighter air, that a diminution of pressure can occur. 

Does this condition obtain in a cyclone to a sufficient 
extent to account for any considerable part of the ob- 
served effects? 

It must be remembered that the existence of a low in a 
cyclone is largely a matter of momentum, and is in large 
measure due to the force with which the outflowing air 
at the top is thrown out, or the centrifugal force of the 
whirling mass. In accordance with the laws ordinarily 
governing the equilibrium of fluids, the heavier mass 
should move in at the lowest level of the lighter mass. 
Now, if condensation of moisture into rain at the upper 
level of a cyclone is the source of its energy, there ought 
to be an inrush of air at the lower level of the area of pre- 
cipitation instead of the inrush that actually occurs at the 
earth's surface. Besides it must also be remembered that 
the precipitation extends often over a region of many 
hundreds of miles in diameter, and expansion distributed 
over such wide areas would probably prove obstructive 



CYCLONES, COLD WAVES, AND TORNADOES 183 

instead of helpful, acting backwards toward the center as 
well as outward. 

Equatorial Over current: The equatorial westerly over- 
current performs a double office; that is, it contributes 
both to the rotary or gyratory movement of the cyclone 
and its translation or progression, and both of these things 
it does by clipping off the upper part of the gyrating mass. 
This process of beheading, while it contributes largely 
to the movements of the cyclone as long as it remains in 
the tropics, becomes almost the only force in operation 
after the cyclone has turned to the poleward and later 
when it has entered on its eastward journey. 

It is quite obvious that if the upper half of the column 
of atmosphere over the site of the gyrating mass 
constituting a cyclone, should be removed contin- 
uously and so rapidly and so completely that its weight 
should be wholly taken from the lower half, an area of low 
pressure would be produced, whose weight would be 
one-half of that of the normal atmosphere. Any removal 
of a less proportion effected in the same manner, would 
correspondingly reduce the pressure in the area of the 
cyclone. 

The principle is well illustrated in the spraying ap- 
paratus commonly used in applying perfumes, in the 
application of medical substances, and in spreading paints 
when this is required on a large scale. The apparatus in 
question consists of two tubes set at an angle in such a 
way that the opening of one is placed just over the open- 
ing of the other. On putting the end of one of these 
tubes into a liquid and blowing into the other, the liquid 
is sucked up and blown out in spray. 



184 SMITH'S ESSAYS 

Now what happens in this case is that the pressure of 
the air is removed from the mouth of the tube in the Kquid, 
and the pressure of the surrounding air on the Uquid 
forces it up through the tube and out in spray. 

Another illustration of the principle may be observed 
wherever a steady wind blows across a mountain crest as 
for instance over the Peak of Tenerifle, or over Table 
Mountain in South Africa. The air on the leeward side 
of the crest in these instances, invariably rises up and 
mingles with the passing winds above. If the leeward 
air is moist, a cloud will be formed from its moisture, and 
though changing momentarily, will seem to be a constant 
cloud clinging to the mountain crest. 

All that was done in either of the foregoing examples, 
was the production of a partial vacuum or an area of low, 
by the force of horizontal trajectory of the air current, 
into which the air leeward of the crest in the one instance, 
and the substance to be sprayed in the other, was forced 
upward by the pressure of the surrounding atmosphere. 

If the cyclone had its beginning over a tropical island 
in the way suggested, there occurred an inrush of air which 
to the extent of its momentum, lifted up the rotating 
mass and constituted its area a low. A cyclone then 
may be regarded as a mountain of atmosphere largely 
upheld or supported by the momentum of the inrushing 
air at its base. 

The top of this mountain is continuously pulled or 
clipped oflF and carried away forward by the upper westerly 
winds if in the tropics, by the upper returning winds or 
antitrades if on the border of the tropics, and by the con- 
stant easterly overcurrent, if in the temperate zones. 



CYCLONES, COLD WAVES, AND TORNADOES 185 

This decapitated mountain, hollowed out at its base 
as it is as regards its gravity by the momentum of its 
upward moving core, constitutes it thus doubly a vast 
*Mow" into which the air around it is continuously pressed 
by the weight of the superincumbent portion of the sur- 
rounding atmosphere. 

It is obvious that if the speed of the horizontal trajectory 
of the prevailing over-current were equal to that with 
which the removed upper part of the cyclone would be 
faUing when it reached the line of severing, or its force 
were equal to the gravitational pressure of the air over 
the cyclonic area above such line, the barometric pressure 
of the area would be that only of the air below this Une. 
Under such circumstances, the pressure in the middle 
temperate zones would be probably about sixteen inches 
instead of the normal thirty. 

But a cyclone resulting from a depression of two inches 
at the center, shading off to zero at the margins, would 
prove to be one of stupendous power. It would seem then 
that the momentum of the horizontal trajectory of the 
prevailing overcurrents is fully sufficient when taken 
in connection with the other forces named, to account 
for all the energy required or employed in the rotation of 
cyclones. In temperate regions this seems to be the only 
source of their energy. 

The Movement of Progression 

But cyclones have also a movement of progression of 
from 8 to 35 or more miles an hour, and that often in the 
face of a wind of equal or greater speed. The cause of 



186 SMITH'S ESSAYS 

such progression, or at least the definite mechanical 
elements underlying it, have not hitherto been explained 
with satisfactory fullness and particularity. 

It has long been known that cyclones take the general 
direction of the prevailing over-currents of the region in 
which they happen to be traveling, but seemingly fatal 
difficulties have always attended attempts at a satisfac- 
tory explanation of the movement. 

Preponderating precipitation of condensed vapor in the 
body of the cyclone in advance of its center, has been 
suggested as a principal source of the energy of its pro- 
gression, but this attempted explanation is greatly dis- 
credited by the fact that in the tropics, where precipitation 
is by far the greatest, the progression is slowest : and it is 
still further impaired by the fact that cyclones, at times, 
cross the entire American continent without noticeable 
precipitation. 

As long as the route of the cyclone is restricted to the 
tropics, the westward trend of the trades below, and the 
antitrades above, might with some show of reason be held 
sufficient to account for the observed progression. But 
after the path of the cyclone has been changed to the 
northward, and more especially in its final journey east- 
ward, no force or at least no character of mechanism for 
the utilization of any force hitherto suggested, will satis- 
factorily account for the actual movement of translation. 
Here again we have to invoke the action of the over- 
current as the efficient cause. The movement is effected 
in this way. 

The continuous decapitation of the cyclone effected by 
the over-current as already described, is necessarily 



CYCLONES, COLD WAVES, AND TORNADOES 187 

accompanied by a dragging action that causes the upper 
part of the decapitated body of the cyclone to lean for- 
ward in the direction of its advance. The air constituting 
the head of the cyclone, as it is being carried forward after 
separation by the over-current, forms in connection with 
the over-current, a perpetual canopy-like structure which 
projects from the front of the upper part of the beheaded 
cyclone. The speed with which this canopy advances 
gives it a power of resistance that arrests the rise of the 
incoming air. 

Unequal Rising of Cyclone Mass 

This inclination or leaning forward supplemented by 
the canopy mentioned, gives to the mass of atmosphere 
drawn into the cyclone in front an advantage over that 
coming into it from the rear. That is, a mass of air 
approaching the cyclone in front can reach a given point 
on the front of the cyclone, in less time than a like mass 
can reach a corresponding point in the rear: in other 
words the diameter of the cyclone will increase more 
rapidly in front than in the rear. This in turn will cause 
a reforming of the cyclone, with the center continuously 
advancing. 

Yet notwithstanding the fact that the cyclone is added 
to faster in front than in the rear, the conditions require 
that it shall maintain the same dimensions. But the 
same quantity of air if not even a greater quantity, would 
be taken up from the body of the cyclone in the rear than 
in front to be dissipated or carried forward above, and 
this would result in a steady loss or falling away in the 



188 SMITH'S ESSAYS 

rear. That is to say, the air would be removed and 
carried up from the after part of the cyclone faster than 
it was added, and from the anterior part of it slower 
than it was added. This would of itself produce a con- 
stant advance of the cyclone. 

Axis and Center of Gravity 

The controlling element, however, in the advance of 
the cyclone would be its rotation around its advancing 
center of gravity. We have just seen how it is that the 
mass of the cyclone is constantly growing or reforming in 
front, and constantly falling away in the rear, and that 
this causes a continuous advance of its center of gravity. 

Then since the center of gravity is continuously reform- 
ing in advance of the axis of rotation, and the cyclone 
must revolve around its center of gravity, it follows that 
the cyclone must continuously advance in order that its 
axis of rotation may continue substantially co-incident 
with its center of gravity. 

As further proof that the decapitation of the cyclone 
which constitutes it a low may be mentioned the fact 
that cyclones move more rapidly over North America 
than they do over Europe. A long range of lofty moun- 
tains, the Cordilleras, extends obliquely north and south 
along the west coast of North America. When the easterly 
over-current encounters this range, a part of the lower and 
slower portions are deflected southwardly down the 
Pacific Coast; the remaining lower portions are forced by 
the stress to rise up, and thus produce a concentration of 
the flow over the mountain range, which necessarily adds 



CYCLONES, COLD WAVES, AND TORNADOES 189 

to its speed, just as the water in a stream passing from a 
deep pool and up over a riffle is made to increase its speed. 
The increase of speed in the water may be observed for 
some distance over the succeeding deep pool; and just 
so the over current or constant easterly, having had its 
speed accelerated by passing aver the Cordilleras, main- 
tains this increased speed across the American continent. 
In consequence of the acceleration of the over-current 
the head of the cyclone is clipped oJ0F more sharply, 
a more marked low is produced and greater energy is 
given to all the movements of the cyclone over America 
than in Europe. 

Why Cyclones Recurve from Continents 

There remains still another important feature of the 
movement of cyclones to be explained, and that is, the 
determining force which causes them to quit their west- 
ward course as they approach or enter continental areas, 
and turn first poleward and then to the eastward. 

The main if not the only force involved in restricting 
the movement of cyclones to the region of the tropics 
during their westward journey, seems to be the trade- 
winds; for as long as the trades have full play, the cyclone 
retains its path in the tropics. It turns polewards only 
on reaching a continental area or the neighborhood of 
one. 

As previously indicated, the friction experienced by 
winds when blowing over land areas, is much greater than 
that over the ocean. So much is this the case that the 
force of the trades over continental areas is almost neutral- 



190 SMITH'S ESSAYS 

ized. Not only is this the case, but the trades over the 
ocean adjacent to continents, as they reach or approach 
the land, blowing as they do obliquely to the westward, 
are dammed back and retarded for a considerable distance 
out to sea. 

As cyclones move westward along the contiguous borders 
of the trades and the doldrums, the upper or antitrades 
are as continuously and effectively pulling the cyclone 
poleward, as the trades are pushing it equatorward. But 
on reaching a continent or its neighborhood, the trades 
having in a measure lulled for the reason named, the 
antitrades, which have gained their momentum from far 
out to sea, and are still vigorous in the upper regions, 
now prevail and lead the cyclone poleward. Then as 
this antitrade becomes the constant easterly over-current, 
it carries the cyclone on its journey eastward. 

Why Cyclones Avoid Mountain Ranges 

At least three other interesting phenomena that may be 
observed in the movement of cyclones, lend strength to the 
view here advanced as to the source of their energy. The 
first of these is their tendency to leave their course and 
swerve away from mountain ranges when their course 
leads them near to and in paths parallel with such ranges. 
The second is the disposition of cyclones to halt on ap- 
proaching a mountain range transverse to its path; and 
the third is their tendency to bend their course from a 
direct line, in the direction of any large body of water 
near the line of their journey. The further well-recognized 
fact that a cyclone displays more energy of movement on 



CYCLONES, COLD WAVES, AND TORNADOES 191 

sea than on land, would serve in some degree to support 
the vievi that the direction of the movement of the cyclone 
is influenced by the freedom of the currents of air that 
support it. 

A cyclone halts at a mountain range running across 
its path, because the air in front is impeded in passing into 
it and increasing its diameter by adding to it in front. 
This will have the effect of retarding the cyclone, either 
until by a continued process of whirling it has thrown itself 
over the obstruction, or what is more likely, until the air 
in front which is destined to pass into the cyclone, has 
accumulated higher up sufficiently to advance the center 
of gravity so as to enable it to rotate over the mountain. 

A cyclone will be deflected from its direct course away 
from a mountain range when passing parallel to it, because 
the air coming in from the side next the range, is hindered 
in its approach, and thus the diameter on the opposite side 
grows more rapidly than that on the near side, and the 
center of gravity and axis of the cyclone are thus carried 
away from the range. 

A cyclone will bend its path toward a nearby expanse 
of water by reason of an exactly opposite condition. Here 
the friction of the incoming winds is less on the side of the 
water than on the land, therefore the side of the cyclone 
next the water grows more rapidly than the other, and the 
center of gravity, together with the axis of rotation is 
deflected in that direction. 

It might be said also that at the point where the cyclone 
recurves, and where the antitrades are gradually over- 
coming the trades, the movement of the cyclone is very 
slow until it has advanced far enough to come under the 
influence of the more forceful easterly overcurrent. 



192 SMITH'S ESSAYS 

The Cold Wave, High or Anticyclone 

In a large proportion of cases, on the inspection of a 
weather map indicating the location of a cyclone, an area 
of high barometer or an anticyclone will be found following 
it. The anticyclone usually follows on the northwestern 
quadrant, less frequently directly in the rear, and occa- 
sionally on the southwestern quadrant. 

Like the origin of the cyclone the origin of the anti- 
cyclone is involved in much uncertainty and obscurity. 
But the fact that the anticyclone so uniformly accom- 
panies the cyclone, would naturally lead to the inference 
that there is some close connection between the two phe- 
nomena. 

The cold waves that are the outcome of the high areas, 
are often to be traced far to the northward, still there is 
reason to believe that they arise out of conditions pro- 
duced by the cyclone, and furthermore a reasonable and 
probable mechanism may be suggested for such origin. 

We have seen that the air is drawn into cyclones at 
their base and thrown out at the top. This would tend to 
produce a ''high" all around the cyclone, and would do so 
if the conditions all around it were the same. But on the 
forward side of the cyclone the prevailing over-current 
carries with it the greater part of the air that passes up 
through its center. Since enormous quantities of air are 
thus loaded onto the advancing over-current, and since 
its speed on being thrown out of the cyclone is much 
greater than it can maintain after moving forward, it 
follows that the advancing mass must spread out at 
greatly divergent angles : and this it does, as shown by the 



CYCLONES, COLD WAVES, AND TORNADOES 193 

divergent movement of the resulting cirrus clouds. On 
the south, that is the equatorial side, the upper rim of the 
cyclone is moving in the same direction as the easterlies, 
and the air thrown out in that direction is largely carried 
forward by the over-current. 

On the north, the rim or upper border of the cyclone is 
thrown sheer against the over-current, and this action must 
result in damming back and heaping up to a greater or less 
extent, the oncoming over-current, thus producing a "high" 
in that situation. On the west or the rearmost side of 
the cyclone, the friction or obstruction of the border would 
probably not greatly affect the air thrown out on the on- 
coming easterly, since friction to the poleward would 
already have cut to considerable depth into the rim of the 
cyclone. It might, however, in some instances, have the 
effect of driving equatorward the area of high pressure. 

It may, however, be suggested that the "high," being 
made up partly of the air of the dry over-current and 
partly of that which has passed up through the cyclone 
and been drained of its moisture, will readily admit of 
radiation from the earth, and this will promote its cooling. 
It is well known that during an eclipse of the sun, the loss 
of heat in the area of eclipse, due to the preponderating 
radiation will cause an outward breeze around such area, 
Here there has been no accumulation of air, and the cause 
of the outflow must be first, the condensation due to 
cooling and then the momentum of the descent of all the 
condensed atmosphere in the area of the eclipse. A 
"high" has been produced simply by condensation. 

Assuming the formation of the "high" in the way de- 
scribed, in what direction will it be dissipated? Toward the 



194 SMITH'S ESSAYS 

north or in the direction of the poles, the winds on all 
sides of the earth must move more or less directly toward 
the narrowing meridians, and to a condition of anti- 
cyclone : to the east is the cyclone forcing back the over- 
current on its northern border, and to the west the 
oncoming easterlies. Only the territory equatorward is 
open, and only in this direction, the continuously forming 
and continuously dissipating "high" can betake itself, 
and this is the course it pursues. 

If there happens to be a mountain chain substantially 
parallel with the outflow of the " high," such a chain will 
operate as one of the banks of a river and cause the air 
to rise up along its sides as the water of a river does, thus 
permitting the colder air to descend and mingle with it all 
along its course. Hence the blizzard, the norther and 
other like streams of cold air to which this movement gives 
rise. 

A further evidence that the anticyclone is due to the 
damming up of the constant easterly, is the fact that the 
speed of this over-current is less on the north side of the 
cyclone than on the south. If the air of the easterly on 
the north side is checked in its flow, or a portion of it 
carried to the southward by the revolving cyclone, the 
effect of this would be to render the easterlies slower on 
its northern side for the remainder would thus be allowed 
a larger space for its movemant. 

The Tornado 

Tornadoes have been so exhaustively studied that 
there would seem to be little left to be developed in regard 



CYCLONES, COLD WAVES, AND TORNADOES 195 

to them. However, their position with respect to the 
cyclones with which they are connected and from which 
they spring, as well as the cause of their rotation in the 
same direction as the parent cyclone, seems susceptible 
of yet further elucidation. 

With great uniformity tornadoes spring suddenly into 
existence in the quadrant, which is in front and to the 
right of the advancing cyclone. While in the tropics or 
subtropics, this point in the northern hemisphere, happens 
to be on the northwest quadrant; but after the cyclone 
has passed into the north temperate zone and begun its 
journey eastward, it is on the southeastern quadrant. 

It may be remarked of tornadoes, that they occur with 
rare exceptions, at the point where the translatory and 
rotatory movements of the cyclone most nearly coincide, 
and where the greatest resistance is met with from the 
extrinsic atmosphere along their pathway. The fact that 
tornadoes nearly always originate in the body or at the 
margin of a cyclone, and that they invariably rotate in 
the same direction as the cyclone, goes far to prove that 
they are fragments thrown off or split off from cyclones. 

As shown in the essay in this volume entitled, '*The 
Birth of a Planet," if a revolving disc could be made to 
disappear leaving a portion of its mass unaffected, and the 
centripetal and centrifugal forces could continue strong 
enough to hold the separated portion in position, this por- 
tion would continue to move around in the same path as 
before, and without at all rotating with reference to the 
central point of the original body. If a man could separate 
himself from the earth, and rise straight up from it, he 
would begin to rotate, his head outtraveling his feet : if a 



196 SMITH'S ESSAYS 

hole were made into the center of the earth into which he 
could sink freely, he would begin rotation, his feet out- 
traveling his head. 

It would seem then, that a tornado is at the beginning 
constituted of air thrown off from the mass of the cyclone, 
since this would account for the direction of its rotation. 
But it may be that the tornado is primarily controlled in 
its rotation, by the deflection of the winds due to the 
rotation of the earth, just as are cyclones themselves. 
Certainly they could not long continue to rotate in an 
opposite direction. 

But in whatever way tornadoes have their origin, they 
must be supplied from some source, with energy equal to 
the vast power they display. It will here hardly suffice to 
say that the source of their energy is the heat given out 
by condensing vapor. The time for the accomplishment 
of such a task is too short. Every move in the working of 
tornadoes is forced in the highest degree, and there is not 
sufficient time available to allow the slow processes of 
equilibrium to be carried out. 

Besides, tornadoes are not invariably accompanied 
by precipitation. In the tornado that worked such fear- 
ful havoc in Louisville on March 27, 1890, there was not 
enough rainfall to lay the dust where the houses fell. 

Can we not then suggest a more probable source for the 
energy of tornadoes. It is the belief of the author that 
we can, and he insists that it is to be found in his decapita- 
tion theory as already described. 

According to this theory a mass of air is thrown out 
from the body of the cyclone at a point near the level 
where the rising air in the cyclone begins to break away, 



CYCLONES, COLD WAVES, AND TORNADOES 197 

and from whatever cause this mass begins to whirl in the 
same direction as the cyclone from which it springs. At a 
somewhat higher level and immediately above this mass, 
a stream of air is moving away so rapidly that it con- 
tinuously carries away the head of the rising tornado so as 
to remove all pressure coming from the air above it, and 
to give it the character of a vacuum. The rush of the air 
up into this vacuum is the source of the tornado's wonder- 
ful power. 

Similar conditions may also obtain in anticyclones, for 
even in connection with the outflow of the air from them, 
tornadoes have been observed of such intensity as to be- 
come waterspouts on passing out over the sea. 

The behavior of tornadoes in the production of cloud- 
bursts and hailstorms is still a matter of controversy, and 
the best that can now be accomplished in the way of their 
explanation, is to formulate an imaginary scheme of their 
operation consistent with the mass of observed facts. A 
developed tornado is an hour-glass-like structure, to the 
extent that it consists of a double funnel, with one bowl 
turned upward and another turned towards the earth, 
the two being connected by a stemlike tube. The lower 
of these is seldom visible, for the reason that its moisture is 
not condensed until it has risen above the constriction. 

Formation of Hailstones 

The tremendous speed of the whirl of the bowl, and the 
intense centrifugal force developed by it, renders the 
upper or inner surface of this bowl well-nigh as rigid as if 
it consisted of stone or metal. In the character of this 



198 SMITH'S ESSAYS 

structure, may be found an explanation of the larger kind 
of hailstones, that is the kind made up of alternate layers 
of ice and snow, and sometimes attaining a diameter of 
several inches. 

The vapor drawn up through the stem of the tornado 
is at first condensed into coarse raindrops and then frozen 
into hail. These hailstones being first carried up and 
then falling back again into the rigid funnel, are caught 
by the upward rushing air from the throttle and again 
carried up covered with moisture to be coated with snow. 
After a sufficient number of such layers have been in this 
way added to the hailstone, it becomes heavy enough to 
break through the wall and fall to the ground. While 
this process is going on, ordinary hailstones in large 
quantities may be formed and thrown out over or through 
the thinner walls higher up. 

The hail that is formed and falls over extensive areas 
and which may continue falling for considerable periods, 
is most probably found in rising clouds, or on the crests of 
atmospheric waves developed in the upper cloud-bearing 
air. Great masses of water may gather in these funnels, 
and finally becoming too heavy to be carried, break 
through and are precipitated in floods, known as cloud- 
bursts. 



EARTHQUAKES AND VOLCANOES 



INTRODUCTORY 

Something over twenty years ago the author contrib- 
uted to the Kentucky Educational Courant, an article 
entitled ** Earthquakes and Volcanoes," in which he took 
the position that the severest earthquakes and nearly all 
volcanoes, are produced by water passing through fissures 
in the bottom of the sea and mingling with incandescent 
matter from beneath the earth's crust. These fissures 
were supposed to be due to the upward bending of the 
earth crust of the ocean-bottom, as it was forced upward 
over the elevated margin of the dry land. The theory is 
not intended to be exhaustive but merely suggestive, and 
as such it has seemed not unworthy of preservation. The 
theory was alluded to in the article on riverflow in "The 
Philosophy of Memory" published in 1899, not so much 
that it was pertinent as to assm^e priority in its suggestion. 

The hypothesis of kataphoresis, that is, the electric or 
magnetic transfer of hea\y substances in the interior of 
the earth may be entirely too bold in the present state of 
knowledge, but the facts it is intended to explain seem so 
obscure as regards their causation that one may be ex- 
cused for going wide of the ordinary path to search for an 
explanation, even upon very sUght indications. 



201 



EARTHQUAKES AND VOLCANOES 

Of all the terrestrial manifestations of the power of 
nature, outbreaks of earthquakes and volcanoes are by far 
the most impressive and terrifying. Men may face the 
destructive carnage of the battlefield, or go dowTi beneath 
the sea to certain death with smiles and song; but when 
the solid earth, the synonym of all that is firm and stable 
begins to sway and open up beneath their feet, the strong- 
est heart fails, and the loftiest courage is changed into fear 
and panic. 

It would be little to the credit, then, of the curiosity of 
man, if strenuous effort had not been put forth, early in 
his career, to ascertain the cause of such upheavals, and 
if earnest speculation had not been indulged as to the 
nature of the forces involved in their production, even 
though such force might appear to be beyond the reach 
of scientific scrutiny. 

Many and probably a great majority of earth tremors 
are susceptible of explanation on simple principles. The 
constant succession of such tremors of the mildest charac- 
ter are in every probability due to tidal forces; while a 
great majority of the more severe, but still comparatively 
mild ones, are due to the sliding and sheering of the 
earth's crust incident to its contraction. 

Any one who has had experience of the settling of the 
walls of a brick building, when its supports have been too 

203 



204 SMITH'S ESSAYS 

much weakened, will not be slow to believe or hard to 
convince, that sliding and crushing arising out of the 
earth's contraction, quite reasonably account for the 
ordinary earth tremor. 

But earthquakes producing certain of the stupendous 
upheavals and explosions that have been recorded, seem 
to require a different explanation. Such unspeakably 
terrible catastrophes as the destruction of Krakatoa in the 
Straits of Sunda in 1882, must have had some other 
origin than the mere sliding and crushing of parts of the 
earth's crust. If we may judge by analogies supplied by 
common experience, they must arise from the contact of 
large masses of water with the molten magma in the 
earth's interior. 

Predisposing Forces 

Before attempting, however, to make a study of the 
application of the forces immediately involved in the 
production of earthquakes and volcanoes, it is well to try 
to attain a clear notion of the forces and conditions exist- 
ing and operating in nature, which lead up to their pro- 
duction. 

The fountain head of all the phenomena in question is 
the secular cooling of the earth. Physicists are sub- 
stantially agreed, that the earth was once an incandescent 
mass, that through untold eons of time, it has been grad- 
ually growing colder, and that it now consists of a central 
incandescent mass, extremely rigid under pressure, and 
covered with a hardened crust somewhere between twenty 
and fifty miles in thickness. 



EARTHQUAKES AND VOLCANOES 205 

From the earliest period of its formation this crust, 
while constantly thickening, has been for the most part 
continuously rising by portions and by turns. A few 
areas, however, of greater or less extent, offer no evidence 
of ever having ceased to rise, and a few others, mostly or 
altogether embraced in the great oceans, afford no evidence 
of having ever ceased to subside. 

But before entering upon a consideration of the ad- 
vanced stages of sea and mountain formation, we may with 
advantage undertake to form a conception of the steps 
by which the earth was set in order for the vast changes 
that have taken place upon it in the course of its long 
history. 

The Beginning of the Seas 

Let us begin with the earth at that period of its history 
when it first became cool enough to permit water to re- 
main permanently on its surface. Before that time all 
the water of the ocean then in the form of vapor, all the 
oxygen of the present rocks, and whatever else could be 
sublimated into a gaseous form, must have constituted a 
part of the enormous weight and mass of the atmosphere. 

But the earth at length grew cold enough for the be- 
ginning of the seas, and this beginning must have been at 
the poles ; for the difference in heat of even no more than a 
hundred degrees between that of the equator and the 
poles must have had some effect, and have exerted some 
influence in the cooling of the earth. The earth where 
the rains first reached its surface, and where the water 
first remained, cooled off more rapidly than at other places 



^06 SMITH'S ESSAYS 

by reason of convection, and thus were formed the begin- 
nings of the solid crust. And this crust made dense by 
the cooKng and loaded more or less with water, settled 
down into the yet molten mass so as to form a basin. 
The water that gathered in this basin gave of its acids and 
promoted chemical combinations that added still further 
to the density of the material of its walls. This process 
continued to extend until the entire earth was at last 
covered with water. The deeper places, however, went on 
deepening, more at first, perhaps, from increased infiltra- 
tion of heavy materials incorporated into the crust be- 
neath them than from any other cause, until eventually 
the continents began to appear above the boundless waste. 

But geologists are not wholly in accord as to the method 
of the beginning and the subsequent deepening of the 
seas. Professor Leconte heads a school which contends 
that the first depressions in the earth's surface that were 
later to become seas, had their rise in the fact that some 
areas of the surface were better conductors than others, 
and that these areas radiated their heat most rapidly and 
settled down to form basins. These basins were sup- 
posed to extend in area and depth until the present rela- 
tions and proportions between land and water reached 
their development. 

But, whatever the particular method or whatever the 
cause of the deepening of the seas, and the elevation of the 
land, it is not disputed that as the land emerged, vast 
quantities of sediment brought down from the elevated 
land, were deposited along the margins of the seas, and 
more especially about the mouths of the great rivers. As 
the depth of this sedimentary deposit increased, the sea 



EARTHQUAKES AND VOLCANOES 207 

bottom on which it rested settled down with the result 
that the level of fusion rose, and a large proportion of the 
lowest part of the thickened crust in such situations, 
became incandescent. And since the igneous rocks form- 
ing the bottom of the main oceans were stronger than 
those constituted of sedimentary deposits, the earth crust 
imder such deposits was left weaker than in other locali- 
ties. 

Meanwhile the crust was everywhere growing thicker 
and stronger as the earth grew cooler and progressively 
contracted. But this crust, especially the outer part of 
it, eventually reached the limit of cooling and ceased 
further to contract. Then as the core became cooler it 
tended to withdraw from the crust, and the crust as it 
followed the shrinking core, was necessarily thrown into 
folds and wrinkles, the larger of which coinciding with the 
weakened lilies of sedimentary deposit, became the moun- 
tain chains. 

Leconte and his school will have it that the lateral or 
horizontal thrust due to the shrinking of the earth's inte- 
rior, is practically the only cause of chains and systems of 
mountains and with certain qualifications this is prob- 
ably true. 

Another proposed explanation has been recently offered 
by Prof. T. J. J. See, which he contends for with great 
insistency. Without having raised an issue insofar as 
the writer is aware, as to the mode of the beginning of the 
seas. Professor See contends that water in vast quantities, 
slowly percolates the ocean bottoms into the molten mass 
beneath the earth's crust. This water is there changed 
into steam by the intense heat, and this produces an ex- 



208 SMITH'S ESSAYS 

pansion of the material with which it commingles, and 
the expanding matter operates as a lateral expulsive force 
and consequently drives the contiguous plastic mass 
away from the lines or points of swelling. This liquid or 
plastic material, he contends, passes out under the adja- 
cent land areas or the more shallow sea areas, and there 
by an upward lift elevates the continental areas with their 
mountains, at the same time producing volcanoes and 
earthquakes. 

Theories Examined 

We will now scrutinize these theories a little more 
closely and ascertain whether or not they comport with 
our notions of probability established by observation and 
experience, when tested by impartial judgment. 

Take first the contention of Professor Leconte. Let 
A. B. C. D. and so forth (Fig. 1) represent cones in a 
section through the center of the earth, and W a depression 
in the base of the cone A, filled with water. It is obvious 
that the deeper the water in the depression W, the lighter 
will be the cone A, other things being equal, since water 
has less than half the specific weight of the solid material 
of the earth's crust. 

Just as soon then, as the deficiency of weight at W, 
ceases to be made up by increase of density somewhere 
in the cone A, between W and the center O, A must begin 
to rise up or to recede from the center. 

In the deepest part of the ocean the water forming the 
base of the Cone A, will have a depth of six miles. Now 
is there any known or possible means by which sufficient 



EARTHQUAKES AND VOLCANOES 209 




Fig. 1. 

weight may be added to the solid material of a cone so 
situated, to make up the difference between the weight 
of six miles depth of water forming its base, and six miles 
of solid material which it displaces, not to mention some 
800 feet T\^hLich indicates the average level of the land 
above the level of the sea. 

The difference in depth between shallow and deep seas 
could not well be due to the difference in facility of radia- 
tion; for after both are cooled, the process of cooling could 
not influence the density. It is not known to be impossi- 
ble, that interstitial deposit in the sea bottom might have 
such effect, but it is in the highest degree improbable. 
The deepest seas are almost invariably far removed from 
the sources and facilities of the greatest deposit. 

The forces invoked by Professor See seem equally to 



210 SMITH'S ESSAYS 

fall short of a satisfactory explanation. Let us concede 
that water does permeate and leak through the solid 
crust forming the sea bottom into the molten magma 
beneath the crust, and that it there expands into steam, 
all of which is quite possible, and we are still a long way 
from a satisfactory explanation. 

Concede that in some way a depression has been pro- 
duced, that a body of water has gathered in the depression, 
that seepage has taken place, and that this seepage has 
been transformed into steam. As soon as this has taken 
place, the expansion of the steam will raise the crust 
where it is lightest; and if the mass of water of normal 
specific gravity and the mass af the cone of which this 
water forms a part, together are of less weight than the 
several neighboring cones, then such cone will be lifted 
up, and not the contiguous or any more distant ones. 

The deeper the water in any place the lighter the cone 
of which it might form a part. In the deepest water also 
would occur the greatest leakage, and therefore unless some 
other influences were involved all the deep seas, whose 
bottoms did not possess enough added material to make up 
for the deficiency due to the weight of the water entering 
into their formation, must diminish in depth until equilib- 
rium should be restored. Nor could any considerable 
deepening of the seas or elevation of the land take place 
under such conditions; for as fast as the crust became 
solid and settled down under the weight of accumulated 
water, it would be forced to rise up, by the expanding due 
to seepage beneath; and under such circumstances a basin 
could be formed only to be destroyed almost as soon as 
formed. 



EARTHQUAKES AND VOLCANOES 211 

Theory of the Author 

The theory the author w ;iild offer in explanation of the 
origin of earthquakes and volcanoes, has already been 
partly set forth in an earlier part of this discussion; but it, 
too, needs to be helped out by an hypothesis which, to 
say the least, must appear somewhat fantastic or at least 
extravagant, and which will be postponed for later con- 
sideration. 

This theory assumes first, as already stated, that in 
some way a system of basins was formed in the surface 
portions of the cooling and contracting earth; and along 
with this basin formation and cooling came a condensa- 
tion of the material of which the crust was composed. 

This condensation was partly due to the contraction and 
partly to the deposit and incorporation of various minerals, 
salts and salt-producing elements held in solution in the 
water. At the same time the rising land areas were con- 
tinuously leached of their soluble elements by the water 
permeating them and afterwards finding its way into the 
sea. This further lightened the forming continents, and 
promoted their elevation. The matter held in solution 
was in large part deposited in the sea bottoms and aided 
in further deepening the sea. Meanwhile the tremendous 
rains of the period produced an enormous amount of 
erosion, and the detritus was ^ddely deposited in the 
deep seas bordering the continents. 

The earth had by this time reached a stage of cooling 
and contraction where the lateral thrust of the crust 
against itself, produced permanent wrinkles and crump- 
lings, and these as a rule would occur along the line where 



212 SMITH'S ESSAYS 

the thick and dense sea bottom crust met the more porous 
and probably thinner and less dense dry-land crust; and 
here also happened to be found the vast accumulations of 
sediment already referred to, weaker in structure than the 
igneous rocks of the remaining crust, and made weaker 
still by reason of the fusing of the deeper portions. 

Now if a piece of cardboard and another of note paper 
be laid on a table and the two be pressed together laterally 
against each other, the note paper will give way before 
the cardboard, and in the note paper near its edge, a bend 
will be produced with its curvature convex upward. 

It is obvious that if there is a plastic or liquid magma 
beneath the earth's crust, and there must be to sustain 
any of the present-day theories, the earth must be in a 
state of substantial isostasy. That is, a cone cut anywhere, 
with its base at the surface of either land or sea, and with 
its apex at the center of the earth, must be of the same 
weight as any other cone cut in the same way, and of the 
same angle. 

Therefore, since the level of the surface of the sea is 
lower by some 700 feet than the level of the surface of the 
land, and since a cone taken from the sea, with its base 
at sea level and its apex at the earth's center, must not 
only be shorter than a like cone taken from the dry land, 
but must also have several miles of its base consisting of 
water, we cannot escape the conclusion that the earth 
crust under the sea, is heavier than the crust of the dry 
land. 

And again; since the land crust yields before the sea- 
bottom crust on lateral thrust, the sea-bottom crust 
must be the more rigid. Mountain chains then, we must 



EARTHQUAKES AND VOLCANOES 213 

conclude, are caused by the lateral thrust of a denser and 
more rigid sea-bottom crust against a less resistant dry- 
land crust. Mountains would be formed in the dry-land 
crust along the sea margins even though there were no 
sedimentary deposits. But the areas of sedimentary 
deposit being the weakest points involved, they are forced 
to rise in the crush and form mountains. 

Production of Earthquakes and Volcanoes 

This brings us to a position where we may consider the 
immediate mechanism involved in the formation of earth- 
quakes and volcanoes. In the accompanying illustration 
(Fig. 2) let S be the sea, M a marginal mountain, Sc, the 
sea-bottom crust, Lc, the dry-land crust and G, the 
incandescent matter beneath the earth-crust, and let it be 
further supposed that these crusts have been forced 
against each other horizontally. 







Fig. 2. 

At M, the marginal sedimentary deposit has been 
elevated by the pressure into a mountain, and while the 



214 SMITH'S ESSAYS 

land crust at the margin of the sea was bending upward 
at this point, one or more V-shaped fissures were 
produced at the apex of the bend, where also the 
flexure is most acute. This fissure or succession of fissures 
might at times extend quite through the crust, and does 
doubtless often reach the softened deeper portions of the 
crust. 

In the under surface of the sea-bottom crust, where 
this begins to bend upwards, inverted V-shaped fissures 
are formed, which in the vast majority of cases do not 
extend through the crust. As these inverted V-shaped 
fissures widen below, incandescent matter which has 
probably been kept more or less rigid under pressure, now 
relieved of this pressure and become liquid, rushes up 
into them and produces more or less shock and tremor; 
or meeting water released by the fracture might produce a 
shock sufficiently strong to set the whole earth trembling. 
Or it may be that the expansion of the mingled water and 
seething lava is so great that it forces an outlet. If it had 
sufficient time this expansion might exhaust itself in pro- 
ducing a slow disturbance of the equilibrium of the 
earth, but when the inertia of the opposing mass of the 
earth is too great to be suddenly overcome the expansion 
seeks a nearby outlet. Upward, therefore, under the 
dome formed of the vast slabs of sea-bottom crust and 
dry-land crust leaning against each other and thus partially 
relieving the underlying magma of pressure, it finds its 
easiest way of escape, not an open way it is true, but 
through material with its density relaxed by diminished 
pressure. Through this half opened pathway it reaches 
one of the V-shaped fissures or a regular succession of such 



EARTHQUAKES AND VOLCANOES 215 

fissures in the crest of the neighboring mountain and 
there escapes, producing a volcanic eruption. 

Volcanic Explosions 

There occur at times, however, seismic explosions of 
such terrific power, that to explain them greater force 
must be invoked than any hitherto mentioned, and in the 
explanation of which it must be assumed that water from 
the bottom of the sea is poured down in great quantities 
upon the molten magma beneath the crust constituting 
the sea-bottom. 

If one will make the experiment of whittling a trough 
out of a block of potato or other convenient fragile mater- 
ial, and then cutting across the bottom nearly to the rim, 
and bending the trough so as to open the cut in the bottom, 
he can easily conceive how a fracture in the bottom of 
the sea, running across a deep depression or trough 
might dash great masses of water against the molten 
material that would rush up from below. The shoulders 
constituted by the borders of such a depression, might 
easily act as a fulcrum in such a way as to create a chasm, 
opening quite through the crust at the bottom of the sea. 

The pressure of the water at the bottom of a sea four 
miles deep would be about six hundred and seventy tons 
per square foot and would have an initial speed on entering 
such a chasm as supposed of about the speed of a cannon 
ball. It is quite clear then, that a vast quantity of water 
could rush through such opening before this could be closed 
by the cooling lava, enough conceivably to produce such 
destruction as that which accompanied the explosion of 
Krakatoa. 



216 SMITH'S ESSAYS 

The Hollow Dome 

It is not necessary to suppose, nor is it possible that the 
Uquid magma, displaced by the expansion due to its 
meeting with the water descending from the sea, shall 
travel uninterruptedly up from beneath the crust of the 
sea-bottom to the craters of the adjacent volcanoes. 
Each particle need travel but a short part of the way. 
It is the wave-like impulse sent along that fills the dome 
and forces the lava up from beneath through the volcano. 

Once the crust of the earth is ruptured, once a fault is 
produced, then even a far away stress might produce an 
upward thrust at the site of such rupture. 

Therefore if swelling should be effected by the leakage 
of water through the sea-bottom crust, it need not be 
considered as necessarily restricted in its uplifting power 
to the immediate vicinity. 

The fact that earthquakes and volcanoes originate or 
are found at the margins of deep seas, and that the largest 
volcanoes and the severest earthquakes are encoimtered 
near the margins of the deepest seas, or about abysmal 
deeps, is accounted for on the principle that the sharp 
bends in such places are most apt to produce fissures and 
that in such situations are most apt to be found, the 
deep troughs whose transverse fracture is best calculated 
to bring sea and interior lava together. 

Long Distance Earthquakes 

It is well-known that when fine or short vibrations pass 
through rigid material into that which is broken or plastic, 



EARTHQUAKES AND VOLCANOES 217 

they overtake each other and become slower and coarser. 

May it not be then that when we find violent upheavals in 
unlooked for places, as at Charleston and New Madrid, 
they have been produced in some such way by a distant 
disturbance? May it not be that shocks starting from 
the Tuscarora Deep and produced by it, have travel- 
ed by means of fine vibrations, along the most 
rigid available path, until on entering a field of weak and 
disconnected sedimentary deposit at one of the places 
mentioned, and then after changing the character of their 
vibrations into coarser ones, have broken out into violent 
upheavals? 

In case of a sudden swelling of the nature of an explosion, 
the inertia of obstructing material would necessitate the 
escape of the displaced material at the nearest weak 
point, even if there were a weaker one farther away. But 
if the stress accumulated slowly, it might produce up- 
heaval on perpendicular lines, even as far away as the 
opposite side of the earth, just as a mass of nitro-glycerine 
slowly burned in the air, expends its force quietly by 
convection, while if suddenly exploded, the inertia of the 
air would resist the expansion almost as if the air con- 
sisted of solid stone. 

It can easily be perceived, then, how the secular cooling 
of the earth, and the contact of water with superheated 
matter beneath its crust, resulting from such cooling, 
may produce both tangential and perpendicular displace- 
ment, and how both might be operative in the same 
and very distant places. 



218 SMITH'S ESSAYS 

Magnetic Transference 

There remains still a most important and interesting 
phase of the movement of the earth crust, which has not 
yet received a satisfactory explanation, and that is, the 
successive rising and subsidence of the earth's crust both 
of the land and the sea already mentioned. 

All the geologic agencies at work, so far as we now 
know, make for the further depression of the most de- 
pressed parts of the earth's surface, and the f luther general 
elevation of the higher parts. It is true that denudation 
of the land has primarily a tendency to lower its level, 
but the detritus is removed only to be carried into the 
sea, and if processes of equilibrium are still going on, the 
increased weight imposed upon the sea bottom causes a 
rise of the land which makes up for the loss of elevation by 
denudation. 

What could then have been the force or forces that 
have caused vast areas of the earth's surface again and 
again to rise up and appear as dry land, often remaining 
so for ages, and then sink down to become the bottom of 
the sea? As many as eighty strata of coal have been 
found one above the other, evidencing an equal number 
of subsidences and elevations during the carboniferous 
age alone, and this must be only a small part of such 
changes. 

In parts the sea-bottom has settled down until it would 
seem that the weight of cones of any given angle taken 
from such places would be lighter than cones of the same 
angle taken from other seas or from the dry land, unless it 
be that the deep sea-bottoms have derived density from a 



EARTHQUAKES AND VOLCANOES 219 

source hitherto unsuspected. In short, on the face of 
things there is a violation of the laws of equilibrium, or 
isostasy as applied to the earth. It is here that I would 
timidly and tentatively venture a suggestion. 

We know that there is an electric or magnetic current 
circling the earth, and rendering it a huge magnet; that 
minerals that once must have been uniformly disseminated 
through the star-dust, have by methods hitherto often 
inexplicable, been gathered into large masses; and we 
know further that electric cataphoresis, or the sublimation 
of metals and their transference from one spot to another 
is a matter of common observation. Can it be then that 
forces from the sun, and possibly other luminaries, are 
transformed by the earth's rotation into magnetic cur- 
rents that cause the shifting of vast metallic masses from 
place to place beneath the earth's crust, in such a way as 
to produce continual alterations and shiftings of specific 
gravity. 

If such an hypothesis should prove true, — and it is 
something more than hypothesis, — we would be supplied 
with a ready explanation of the cause of abysmal deeps in 
the sea, and of the numerous successive elevations and 
depressions of both the sea and land areas of the earth's 
surface. 



THE BIRTH OF A PLANET 

OR 

A CRITICISM OF THE NEBULAR HYPOTHESIS 



INTRODUCTORY 

The principle advocated in this essay first impressed 
itself on the mind of the author, while engaged in the 
study of whirlwinds and tornadoes. 

Since whirlwinds are found to gyrate either from right 
to left, or left to right and independently of the planetary 
circulation, the conclusion was reached that the whirl 
must be inaugurated by a faster portion of the air moving 
around a slower part with which the faster part is travel- 
ling. Extending the application of the principle, it ap- 
peared probable that tornadoes are tangential offshoots 
of a gyrating cyclone, and this conclusion led up to the 
view that all subsidiary cosmical bodies that rotate in the 
same direction as their principals, must have been con- 
stituted of masses thrown ofif from their principals at 
a tangent. 

The principle accepted, the conclusion was unavoid- 
able, that planets and satellites, since they rotate in the 
same direction as their principals, must consist of masses 
carried off from the parent bodies, and not merely aban- 
doned by them, and that these bodies now move in larger 
orbits than when a part of the parent bodies. No other 
method of accomplishing this appearing, the intervention 
of comets alone seemed to meet the conditions. 

The author having small hope that the notion would 
ever be regarded as anything but a fancy, made little 
effort to secure it a hearing, until after a dozen years 

223 



224 INTRODUCTORY 

from the time of its publication he was most agreeably 
surprised to learn that the idea had been entertained and 
elaborately developed by so high an authority as Pro- 
fessor T. J. J. See, whose views on the subject have re- 
ceived respectful mention in the New Encyclopedia 
Brittannica. 

The contention of such an origin as is here assigned to 
satellites and planets does not in any way contravene the 
nebular hypothesis in its essential features, but only 
supplements it in that regard. 

The conception of the origin of planets by capture, is 
not without its difficulties, but it appears to be less im- 
probable, and more consistent with known facts than 
the accepted view, which, indeed, appears to contemplate 
a state of facts quite impossible. 



THE BIRTH OF A PLANET 

OR 

A CRITICISM OF THE NEBULAR HYPOTHESIS. 

The nebular hypothesis proposed for the explanation 
of the origin of the various heavenly bodies, was first 
suggested by the philosopher, Des Cartes. In his view 
the sun and planets grew out of eddies or vortices in a 
primitive star dust, which by accretion were enlarged into 
these celestial bodies as they now appear. Later Sweden- 
borg formulated a cosmogony based on a conception of 
vortices. Some sixteen years later, in 1750, Thomas 
Wright published a book on the same subject, which Sir 
George Darrvdn characterizes as preternaturally dull, 
though Kant, the great German philosopher, acknowledged 
that it had been helpful to him. 

Kant toward the last quarter of the sixteenth century 
propounded a much fuller theory than any of his pre- 
decessors had done and indeed developed all the essential 
portions of what is known as the nebular hypothesis. 

In 1796 the great Laplace set forth a theory little 
different from that of Kant, though it is believed that he 
had never read Kant's works; however, since that time 
the theory has been almost universally associated with the 
name of Laplace. 

225 



226 SMITH'S ESSAYS 

Facts in Its Favor 

The facts that favor this hypothesis are both numerous 
and significant, and of its general truth there is scarcely 
ground for doubt. In the first place there are from two 
hundred to three hundred planetary bodies known to 
belong to the solar system, all rotating in the same plane 
and in the same direction, with the exception of the 
Satellites of Uranus, which by some means have been 
caused to rotate at a very considerable angle to the com- 
mon plane of the system. 

Between Mars and Jupiter are a large number of satel- 
lites revolving around the sun, that are possibly the rem- 
nants of a nebulous ring which failed to become a planet 
and broke up into these smaller bodies. 

The probability that such an arrangement as that just 
described and observed to exist among the planets and 
satellites of the solar system, could have been brought 
about by a fortuitous aggregation of nebulous vapor, when 
tested by the doctrine of chances, is almost infinitely small. 

Again, it has been ascertained that the sun is now 
diminishing in diameter by about four miles in every 
century. If this has been steady and continuous in the 
past, forty-seven million years ago, the sun must have 
occupied the space the earth does now, and some time in 
the past must have extended beyond the orbit of Neptune. 

Observations effected by means of the telescope, and 
still more effectively through the instrumentality of 
photography, have also given increased probability to the 
theory. Astronomers have discovered numerous nebulae 
in various stages of progress toward the formation of suns. 



THE BIRTH OF A PLANET 227 

Some of these nebulae have been seen without nuclei, 
others have presented nuclei more or less translucent, 
while still others have revealed extensive nucleus forma- 
tion opaque to the light of other luminous bodies. 

Another feature that favors the theory is the central 
heat of planets. It is entirely consistent with the hy- 
pothesis that planets should begin cooling off at the sur^ 
face, as is evidently the case with Jupiter, the earth, and 
the moon, while the interior mass remains incandescent, 
as is the case with at least the earth and Jupiter. 

Difficulties of the Hypothesis 

Not to mention the irregular orbits of the satellites of 
Uranus, which may well have had an accidental cause, 
there still remain some other difficulties in the way of the 
acceptance of this theory; but there is so much in its favor, 
and philosophers have been so completely baffled in 
devising any other probable mode of origin for planetary 
systems, except that of direct creation, that the world 
generally has accepted it on authority. 

Beside the difficulties in the way of the acceptance of 
the theory that have been suggested by various investi- 
gators, there remains one not hitherto pointed out, that 
seems to require a material modification of its statement. 

This arises out of the fact that the various planets and 
satellites rotate on their axes in the same direction as 
what are supposed to be the parent bodies — the very fact 
that has probably been most relied on to prove the theory. 

Orbit Must Have Been Enlarged 
This rotation about their axes on t e part of planets 



228 SMITH'S ESSAYS 

and satellites could be brought about only by their having 
been thrown off to some distance from the position they 
occupied relative to the parent body as assumed for 
them in the hypothesis. The earth, for instance, could 
rotate on its own separate axis as distinct from that of the 
sun, only by being caused to move in a larger orbit than 
that described by it while it was still a part of the sun's 
mass; but it could not do so while retaining the same 
orbit or moving in one of smaller diameter. 

If a rod be held in the hand by one end then let fly in a 
straight direction after having been swimg rapidly over 
from behind forward, it will begin to rotate as soon as it 
leaves the hand. The reason is that when let fly the 
distant end was moving more rapidly than the near end, 
and so, trying to out-travel it, had to pass around it and 
thus inaugurate rotation about the axis. 

Likewise when a wheel or disc is revolving the outer 
parts are everywhere moving faster than the parts just 
within them, and if a fragment happens to fly off, the 
outer part of the fragment will tend to run around the 
inner and thus rotation will be inaugurated. 

In the character of motion called linear or translatory 
motion, as observed in a rotating body the motion of 
every particle is greater than that of any other particle 
nearer the axis of rotation. But every particle of a 
rotating body has also another motion known as the 
angular motion, and this is the same for every particle in 
the revolving body, no matter where situated. 

Thus a particle near the axis of a revolving body may 
move but one foci a minute, while another at the circum- 
ference may mo e a mile in the same time, but they both 



THE BIRTH OF A PLANET 229 

pass through the same angle. It is obvious that if a 
fragment in a revolving body situated at any point, should 
be freed from the mass of which it forms a part, and the 
same linear and the same angular motion should be pre- 
served to each of its particles that such particle had 
before the separation, the fragment would simply con- 
tinue to go around in its path, without rotating on its 
axis in either the one or the other direction. But if the 
fragment should be drawn closer than before to the axis 
of the body from which it had separated, it would revolve 
in a direction opposite to that of the original body; while 
on the other hand, if it should be thrown farther from the 
center, it would rotate forward in the same direction as the 
original mass. 

Or to give one more and a homely illustration: if two 
horses are running on a small circular race track, the 
outside one must run distinctly faster than the one on the 
inside in order to keep abreast of it. The outside one can 
run a httle faster than the inside one without ever running 
around it. But let them now fly the track at a tangent, 
running side by side in a straight line, each keeping up 
the same speed as before. They will thereupon if fastened 
together, be seen to be revolving around each other in 
the same direction they maintained while running around 
the track, that is the outer one running around the inner 
one. 

With the foregoing illustrations in view, let us now 
attempt to carry out the parallel, and ascertain what must 
occur with a nebulous ring left in space by the contraction 
of a central mass; how it could collect into a globular mass, 
and how it could inaugurate rotation. 



230 SMITH'S ESSAYS 

Let us take for example, the orbit of Neptune. The 
orbit of this planet is nearly eighteen billion (18,000,000,- 
000) miles in circumference, and the particles of matter 
constituting the nebulous ring out of which the planet 
was formed, must on the average have traveled at least 
half that distance in order to get together and form the 
planet; furthermore they must have traveled in the 
same orbit in order to pick up all the material of the ring. 
But what was it that started the aggregation, and what 
force carried the initial nucleus onward in its path in 
order that it might pick up the rest of the ring? 

It would not sulEBce to assume that any inconsiderable 
part of the ring became accelerated and hastened around, 
driving the remainder of the mass before it to be massed 
into a new planet, for the shock of the concussion of the 
faster moving with the slower moving parts would soon 
arrest the excessive motion. While, on the other hand, 
if a part should become retarded or arrested in its prog- 
ress, unless such part should constitute a very large 
proportion of the total mass, this part, if it did not fall 
into the sun by reason of its loss of centrifugal force, 
would soon again be set into rapid motion, as it might be 
overtaken by the after-coming mass of particles. 

It requires one hundred and sixty-four of our years for 
Neptune to revolve once around the sun; and light itself 
would require three years to make the journey. How 
long a period, then, would be required for one part of a 
nebulous ring to leave the part next behind it, to move 
around in such an orbit, bring up the rest and overtake 
that part which had been left behind. 

Furthermore, it is to be considered that all this is to be 



THE BIRTH OF A PLANET 231 

accomplished in the absence of any known or suspected 
cause of acceleration in the one case or retardation in the 
other. 

But it is nowhere suggested in the nebular hypothesis 
that any part of the rings, or any of the existing planets, 
fly oflF at a tangent, or that they in any way recede from 
the parent bodies; and if they do not, we have seen that 
it is not possible for them, even should the particles get 
together in planet forms, to take on rotation about their 
own axes. Yet this must have happened in the case of 
all of the nearly three hundred known globes constituting 
our solar system, if we are to accept the current statement 
of the nebular hypothesis. 

The inaugiu^ation of rotation presents another diflSculty 
in view of the principles we have just sought to confirm. 
A planet or satellite established in the way supposed, 
maintaining its relative position toward the parent body, 
ought always to keep the same side toward that body, as the 
moon does toward the earth. It is certain they 
never came closer than when they began, for if that were 
the case, they would now be revolving in a direction 
opposite to that of the parent globes. 

It may be suggested that the globules formed from the 
breaking up of Poincare's rings revolve in the same direc- 
tion as the original disk without entering into a larger 
orbit, but it must be remembered that the ring in Poincare's 
experiment is moving in a resisting medium and that 
when such a ring breaks up, its outer rim is moving faster 
than the inner, and therefore has more momentum than 
the inner and so moves around it, overcoming the resist- 
ance of the surrounding fluid. 



232 SMITH'S ESSAYS 

Modification of Sir George Darwin 

Sir George Darwin has ventured the startKng sugges- 
tion that the moon was at first lifted up on the earth as a 
tidal elevation, and then thrown off into space. Now, 
this would meet the rotational difficulty as far as the 
satellites or the planets near the sun are concerned, but 
what tidal elevations could be produced on such distant 
planets as Neptune or Uranus, or even Saturn or Jupiter? 

By the time the lines of the sun's attraction reach even 
the earth, they have become so nearly parallel that the sun 
can raise only two-fifths as much tide as the moon, if not 
far less still, although twenty-five and a half million times 
heavier. But before they could reach Uranus, which is 
more than thirty times as far away as the earth, the Unes 
of attraction must be so nearly parallel that the tide gen- 
erating force would be practically obliterated, and the 
tides become almost a vanishing quantity. 

But Professor Darwin does not assert a tidal origin for 
primary planets. On the contrary he declares his belief 
that from the beginning they revolved in substantially 
the same orbits as at present. 

Suggestion of Captured Comets 

Would it, then, be too wild a dream to imagine that 
sometime in the earliest ages, or somewhere in the far 
stretches whence eternity launched the suns into infinity 
and whence our eternal flight has brought us, space was 
peopled with cometary bodies more abundantly than now, 
and to suppose that now and then they passed near enough 



THE BIRTH OF A PLANET 233 

to the shrinking suns to gather to themselves a part of the 
nebulous mass and that, carrying such mass some distance 
away, they joined it in revolving as planets around the 
parent body? 

A comet striking the nebulous border of a sun in a 
direction opposite to that of its motion would be checked 
or arrested by the force of the collision, and might fail to 
carry away any part of such border, but on the contrary 
would fall into, and be lost in the sun's mass. So if the 
comet should strike across the direction of motion of the 
still lens-shaped sim, it might escape, boring through and 
carrying away only a small portion of the nebulous mass. 
But if it should plow into a nebulous border in the direc- 
tion of its motion, when the border was moving but little 
slower than the comet, it might be that the comet could 
gather to itself a portion of the border, carry it far enough 
away to set up a movement of rotation, and then continue 
to revolve with it as a planet around the body of the 
giant captor. 

But after all one might be tempted to suggest and 
might be excused for suggesting that worlds have a season 
to bring forth, as do animals and plants, and that in their 
proper times and seasons, fixed in the infinite councils, 
they drop their ripened fruit of young worlds into space. 



THE PHILOSOPHY OF MONEY 



INTRODUCTORY 

The diversity of views that men adopt of the same 
subject-matter while furnished with virtually the same 
sources of information, is a question of distinct psycho- 
logic interest. The causes of this are not far to seek nor 
so obscure as might at first blush appear. They are 
chiefly two and both of them forms of bias. The first is 
that due to hastily formed conclusions largely directed 
by self-interest, and the second and most effective to 
early training. 

If one desires to ascertain a person's political, economic 
or religious views, he may with fair accurateness conclude 
that they are those of his parents or early teachers, and 
the greater the ignorance of the community the more 
uniformly is this the case. In economic matters the 
moving force in action as well as conviction among those 
who act or think for themselves at all, is largely based on 
seK-interest. It is doubtless self-interest mainly that has 
obscured the money question from the beginning of history. 

The author himself may in this matter be the victim of 
all the short-comings that he fancies he sees in others; 
but whether this be true or not, it affects neither the facts 
nor the reasons offered in support of his views in this dis- 
cussion. 

The method of ascertaining the law of the disappearance 
of the precious metals, and the definite numerical relation 
of money units to unit-worths of vendibles in various 

237 



238 INTRODUCTORY 

countries, here set forth, have never before, insofar as 
the author is aware, received attention. The calculations 
found necessary have cost much labor and time, but they 
yet lack not a little of being strictly accurate, and much 
research remains to be made along the same lines. It is 
believed, however, that the investigations whose results 
are here set forth cannot fail to throw important light 
upon one of the most vital questions of the day, and to 
prove distinctly helpful to all who may have to deal with 
the question of money in its practical as well as scientific 
relations. 



THE PHILOSOPHY OF MONEY 

Few subjects connected with human affairs have elicited 
closer study, invoked more extensive investigation or 
aroused more persistent controversy than the nature, 
office and regulation of money. 

And although the employment of money antedates 
both history and civilization, if we may judge from the 
heated controversies of recent years as well as the uncer- 
tainty as to the near future, its laws are still very far 
from being rightly understood. It is here proposed to 
contribute somewhat in the way of original suggestion 
in aid of a fuller and more correct understanding of certain 
important underlying principles of money that seem 
hitherto to have been largely overlooked. 

In order to arrive at a satisfactory understanding of the 
philosophy of the question, it is indispensable to attain 
at the outset, to a correct definition of the term money. 
A favorite definition of money is '*a valuable thing em- 
ployed in commerce to facilitate the exchange of commodi- 
ties." I would, however, propose a modification of this 
definition, and instead would define money as *'a thing to 
which the value of articles to be bought or sold has been 
delegated in order to facilitate their exchange." 

As a pre-requisite to a right understanding of either of 
the given definitions, we need to attain to a right notion 
of the primary or fundamental significance of the term 

239 



240 SMITH'S ESSAYS 

"value." Value may be defined as "the estimate placed 
upon one thing as compared with others, with reference 
to the position such things hold in human desire." This 
idea is embraced in the term "estimatio" the Latin word 
for value. 

But a still deeper significance attaches to this idea of 
comparative estimate. On a far advanced analysis if 
not a final one, value in its basic aspect, may be regarded 
as the measure of the tension or stress of human desire 
directed to or concentrated upon any particular thing. 
What the ultimate basis or cause of such desire may be 
is not material to our argument; it is enough to know 
that it exists. 

The term "weight" in the domain of physics appears to 
aflFord a fair counterpart to the word value in the realm 
of mind. Weight may be defined as the measure of resist- 
ance to the pull of gravity on a particular mass. A mass 
of matter falling to the earth has, strictly speaking, no 
weight. It is only when the attraction is resisted or 
opposed; that we can in strict truth say that a body has 
weight. 

Now as to qualities or attributes that give rise to value, 
it is not enough that a thing be useful, or even both useful 
and desired, in order that it shall possess value. Air, 
water and sunshine, as often pointed out, are useful in the 
highest degree and universally desired; but by reason of 
their great abundance and facility of attainment, there is 
as a rule no concentration of desire on any particular part, 
and as a consequence they are not appreciably valued. 

But if one of them should be reduced to a quantity 
materially below the requirements of men's needs, it would 



THE PHILOSOPHY OF MONEY 241 

at once become extremely valuable. What would men 
not give for the last cubic yard of air, or the last gallon of 
water? It is manifest, then, that neither the scarcity nor 
usefulness of a thing, nor the amoimt of labor or cost 
involved in its production, is an element of its value, 
except insofar as any or all of these may affect its scarcity 
or abundance, or may serve to diminish or increase human 
desire for it. 

As a general rule the value of things is regulated by the 
amount of human labor or humanly-directed labor it 
costs to produce them. But when we consider the great 
value placed on old stamps, ancient books, heirlooms and 
the like, in which the labor involved is a neghgible element 
of the cost, and that of bits of meteorite, whose production 
cannot possibly involve human labor, we cannot fail to 
perceive that labor is not an indispensable element of 
value. 

On the other hand, we see many things that have been 
produced with much outlay of labor, which are yet with- 
out value, because they have gone out of fashion, in short, 
simply because they are not desired. Men, as a rule, 
bestow labor upon things because when produced such 
things are valuable, and it is not that they are valuable 
simply because labor has been bestowed upon them. 

DiFFEBENT KiNDS OF VaLUE 

It is evident then, that if this is a correct view of the 
meaning of value, an object may possess as many differ- 
ent values or kinds of value as it may have kinds of desir- 
able qualities or properties, provided these are separable. 



242 SMITH'S ESSAYS 

For example let two bullocks be taken and trained as 
oxen. As beef cattle they were worth say twenty dollars 
apiece; trained as oxen they are worth say thirty dollars. 
But these values are just as distinct as if they belonged 
to wholly different kinds of animals. The introduction of 
some other form of power better and cheaper than ox 
power, might render these cattle not worth their keep as 
oxen. They will then have lost their value as oxen, and 
will fall back on their value as beeves. But their value 
as beeves will remain wholly unaffected by their value as 
oxen. 

The same may be said of a gold watch or ring. Either 
of these may have a use value, an antique value or senti- 
mental value, each or all of which may be destroyed with- 
out in the least affecting the commodity value of the 
gold from which they are manufactured. 

Delegated or Representative Value 

The values we have been here considering have all been 
based upon some quality, property, or attribute of the 
object itself which caused it to be desired. There is one 
form of value, however, that has no such basis, but is only 
representative of the value attaching to other objects 
that are in and of themselves desirable. 

It is this character of value that attaches to various 
indifferent materials and constitutes them money. The 
value thus attached and constituting money is wholly a 
representative or delegated value. And just here a dis- 
tinction is to be made between things that represent 
objects in kind, and money that represents the value of 



THE PHILOSOPHY OF MONEY 243 

such things. For example, warehouse receipts, bills of 
lading, and the like, are only particular representatives 
or evidences of ownership, while money represents the 
value of things in a general way, though severally and 
not collectively. The owner of a warehouse receipt is the 
owner of the particular thing the receipt represents, but 
the owner of money is not the owner of any particular 
thing that the money represents. The money represents 
no particular thing but only so much of its value, or so 
much of the value of things in general. 

The Material of Money 

The material that may be endowed with the function 
that constitutes it, money, may or may not possess the 
qualities or properties that make it of itself desirable and 
give it a value outside of its delegated value as money. 
Among primitive peoples, it was indispensable that the 
money material should have a commodity value, for 
primitive man could not rise to a conception of value in 
the abstract, or of value as separate from an object having 
in itself desirable qualities, just as he could not conceive 
of energy apart from some concrete tangible object. And 
many there are who still can do no better. 

Primitive man's first selection and his only notion of 
money was a something already held valuable because it 
was desirable for ornament or use and possessed consider- 
able value in a small compass. It was thus that strings 
of beads, pretty shells, silver and gold, all of which were 
simply ornaments or material for ornaments, came to be 
used as money. But all the while their value as money 



244 SMITH'S ESSAYS 

was wholly different and distinct from their value as 
commodities, however little that fact might then have 
been perceived. 

A delegate or representative may be elected to the 
British Parliament or the American Congress without 
having a right at the time to vote in his home district or 
at the polls at all, but, as a representative with delegated 
powers, his vote is equal to that of any other. It is com- 
mon for the unthinking to speak of fiat money in dis- 
paragement, as if there could be any other money than 
fiat money. A representative is uniformly the creature 
of fiat, and the validity of money always rests either on 
the fiat of law or the fiat of social custom. 

It matters not in the least what the material may be 
that is made the instrument of the money function; it need 
not have any commodity value whatever. The function 
might be conferred on slices of whirlwind, if they could be 
properly limited, standarded, preserved, and identified. 

Money the Denominator and Standard of Value 

Money is often designated as the standard and denomi- 
nator of value, and, also, as the measure of value, as 
incidents of its office of facilitating exchange in commerce. 
It may well be called the measure and denominator of 
value, but it is not easy to conceive how it may properly 
be called a standard of value. It is rightly called the 
measure of value because it is employed in dividing or 
measuring-off vendibles into units of equal value. It is 
the denominator of value, because it gives to these parts 
the name or denomination of the dividing unit, such as 
dollar-worth, poundworth, and the hke. 



THE PHILOSOPHY OF MONEY 245 

But how can it be truly said that money is the standard 
of value? The word, "standard" arose from the Roman 
custom of planting spears at certain distances apart, and 
then filHng the space between with a line of soldiers. 
Later the word in old French came to be "estandurt," 
meaning standarded or limited as by standards or markers. 

There may be then a standard gold dollar or a standard 
silver dollar in the sense that it is standarded or limited 
to a given material, weight, fineness, breadth, thickness 
or imprint; and such a dollar, or one made of any other 
substance, could well be made and denominated a measure 
of value, or a so-called standard measure of value, but 
how it could put boiuids to value is not so easy to per- 
ceive. 

The Dollar and the Dolk^r-Worth 

A feature of the philosophy of money that has not 
hitherto been considered, insofar as the \sTiter is aware, 
is the numerical relation of the unit measure of value to 
the unit measure of vendibles. The number of units into 
which vendibles are divided, must always be greater than 
that of the representative or dividing unit. If every 
voter had a separate representative in a delegate assembly, 
legislation would in nowise be facihtated or lessened in 
cost. 

And not only would there be no economy in having a 
dollar of money for every dollar- worth of valuation of 
vendibles, but the very organization of the human mind 
forbids such an arrangement. The reason for the existing 
difference is that men require the largest practical revenue 



246 SMITH'S ESSAYS 

from their holdings, while money is wholly sterile and 
unproductive when not in use. It neither reproduces nor 
grows when not loaned out or employed in trade. If, 
therefore, one-half of the world's wealth should exist in 
the form of money, then one half of the world's ownings 
must be all the time continuously idle and wholly sterile 
and wholly unproductive for that money must be all the 
time in the hands of some one. If one-tenth of the world's 
holdings were in money, one-tenth of all of men's posses- 
sions must remain constantly barren. 

Now the human mind, insofar as the western world is 
concerned, is so constituted that whereas men are willing 
as a rule to have a part of their possessions lie idle and 
unproductive all the time or all of them part of the time, 
the average man is never willing to have so much as half 
of his holdings lie sterile all the time, or all of them as 
much as half of the time. Hence in every land and in 
every age, there are found fewer unit-measures of value 
than unit-worth's of vendibles, fewer dollars than dollar- 
worths. 

It is easy to find what proportion of the time the people 
of any given country are willing to have their holdings lie 
wholly idle and unproductive in the way described. It is 
required only to divide the number of unit-worths of 
wealth in a country by the number of money units con- 
stituting its money stock, and then to divide the result- 
ing quotient into the number of days in a year. Thus if 
there is in any country one dollar of money to every 
thirty dollar-worths of wealth, that would indicate that 
the average man of such country is willing to have his 
entire ownings lie idle for one-thirtieth of the time, or about 
twelve days in the year. 



THE PHILOSOPHY OF MONEY 



U7 



The ratio varies great h^ for different periods and for 
different countries, as will appear from the accompanying 
table. 

Table of Ratios of Dollars to Dollar- Worths in 
Various Countries 





o 
o 


3 


00 


00 

T— 1 


o 

00 


00 

oc 


GO 


o 

00 


o 

00 
00 

T-H 


o 


I— 1 


o 

1—1 

I— 1 


Great Britain 


29 




%% 


30 




51 








66 


60 


87 


France 




16 






29 










20 


36 


28 


Germany 




















31 


38 


29 


Austria 




















40 


49 


37 


Italy 




















22 


49 


33 


Spain 




















34 


60 




Portugal 
















" 




33 


27 


24 


HoUand 




















28 


36 


33 


Belgium 




















27 


27 


35 


Switzerland 




















38 


73 




Russia 




















33 


27 


35 


United States 














27 


25 


35 


29 


43 


42 


AustraUa 




















45 






Canada 




















98 







Thus in Great Britain, in the year 1700 the ratio was 
29; in 1910 it was 87. In France it was 16 in 1705, and 
though it rose to 36 in 1900, it was still 28 in 1910. In the 
United States it was 27 in 1849 and about 50 in 1910. A 
similar disposition of the ratio to advance is shown in 
nearly every country of the western world, notwithstand- 
ing a number of very considerable fluctuations. The 
significance of this advance is that, keepmg pace with the 



248 SMITH'S ESSAYS 

progress of commercial development, each money miit is 
made to perform a constantly increasing quantity of work. 
It means that men are progressively disposed to hoard 
money less and to keep it more actively in circulation as 
commercial activity and trade facihties increase. 

But a feature of monetary statistics not so easily ex- 
plained IS the fact that the ratio differs so greatly in diiBFer- 
ent countries. Thus the ratio in the year 1900, as shown 
by such statistics as are available, ranged from 73 for 
Switzerland to 27 for Russia, Portugal and Belgium. In 
1910 the range was from 87 for Great Britain to 24 for 
Portugal. A strictly accurate average for all countries 
could be obtained only by calculations based on a process 
of alligation. The average may, however, be safely placed 
at 40, certainly not below 39. 

This great diversity of ratio is diflBcult satisfactorily to 
explain. It may be partly ascribed to errors of statistics 
or to different methods of estimating wealth; partly to a 
disposition of the people to hoard money, as in France; 
partly to the prevalence of barter in some countries; and 
in some cases it may be partly due to classing as currency, 
gold that is kept in war chests, such gold not being em- 
ployed in trade and therefore not contributing its pro- 
portionate share in the inflation of prices. At present, 
neither the ascertained facts n.r available space suflfice 
for a satisfactory discussion of this feature of the subject. 
This question of ratio, however, as just considered, will 
be found to have a distinctly weighty significance when 
we come to consider the future of prices. 

But before entering upon that phase of the subject, it 
will be necessary to ascertain the law of the disappearance 



THE PHILOSOPHY OF MONEY 249 

of the precious metals; that is to say, their disappearance 
from the commercial nations of Europe and America, 
whether this disappearance be due to wear, to consump- 
tion in the arts, to shipwreck or to transportation to 
India and other eastern countries, whence gold at least 
never returns. 

The Law of the Disappearance of Gold 

In order to ascertain the law by which the disappearance 
of gold and Ukewise of silver is determined, we begin with 
the earliest continuous records of the money stock of the 
world and of the annual production of the mines, and 
assume a percentage of annual disappearance. At the 
end of each year the calculated loss at the assumed rate 
is to be substracted from the total existing money stock 
of the metal under investigation, and to the remainder 
thus obtained is added the amount of the metal mined 
for that year. 

Thus in the year 1600 there was in existence in the 
Western World, according to the best available statistics. 
$144,650,000 in gold. Subtracting from that sum 1.66 
per cent, or about 1-60 each year as the assumed percentage 
of annual disappearance, and then adding to the remainder 
the quantity mined for that year, our rule gives us for 
the year 1700, the date of the next succeeding estimate 
recorded, $367,576,000. Soetbeer's statistics for the same 
year give us $363,750,000, showing for the rule the 
comparatively small error of only $3,826,000 in a century. 
We may rightly conclude, then, that during the Seven- 
teenth Century the loss of gold to the Western World was 



250 SMITH'S ESSAYS 

slightly more than 1.66 per cent or one-sixtieth part per 
annum. 

From 1700 to 1800 the percentage of gold disappearing 
was somewhat higher, being a small fraction less than 
two per cent per annum. Thus in the year 1700, as 
already stated, the stock of gold was $363,750,000. Ap- 
plying the rule on a basis of a loss of two per cent per 
annum, we have in the year 1800, $580,623,000. But 
Soetbeer gives us for that year $582,000,000, which indi- 
cates that we are in error by $1,377,000 for the century, 
due to the assumption of a percentage of loss slightly too 
large. 

From 1800 to 1848 gold disappeared at a rate possibly 
very slightly less than during the previous century, the 
figure being very close to 1.95 per cent. 

But, following upon the rich discoveries of gold in 
California and Australia, there occm-red a sharp increase 
in its disappearance so that from 1848 to 1860 the rate of 
disappearance was above 23^ per cent, but less than 3 per 
cent. From 1860 to 1900, the loss gradually became less 
until at the present time the annual disappearance may 
be placed at a figure slightly less than 1.75 per cent, and 
the rate of proportional loss appears to be steadily de- 
creasing. This is no doubt mainly due to the storing of 
the metal and issuing certificates against it. 

Pursuing the same method in regard to the loss of silver, 
we find that this metal is now disappearing at a rate of 
close to 2.5 per cent per annum. 

Ancillary or Credit Money 
The influence of money on prices is the same, whatever 



THE PHILOSOPHY OF MONEY 251 

the form of that money may be so long as it remains in 
use. Every unit of actual money will carve out for itself 
its proportional number of unit-worths of vendibles as 
soon as it is assimilated into the general circulation. 
This is true not only of bank Oi* government issues of 
paper money, but it is true also of loans of credit by banks. 
When a bank loans its credit to its patrons, that is, when 
it makes loans without having the corresponding money 
on hand, such loans exercise all the functions of money 
in causing a rise in prices, so long as they continue out- 
standing. The borrower, being required to pay interest 
on his loan, will not leave it idle, but will go into the 
market and to the the extent of his loan, bid up prices. 
When the loan is repaid by money taken out of the general 
circulation, its influence on prices ceases. 

It may be laid down then, as a fair test of money that, 
whatever by its increase diminishes the value of the 
money unit, that is, causes it to buy less, is money: while, 
on the other hand, whatever by its increase enables the 
money unit to buy more, is commodity or vendible. 

The Future of Prices 

Having passed in review the chief factors that every- 
where and permanently affect prices, we may now venture 
upon a more or less definite prediction as to the state or 
range of prices in the future. 

Of course, there are other factors than those mentioned 
that affect prices at particular times and in particular 
places. Among such influences are tariffs, monopolies, 
panics, untoward or favoring seasons, changes of fashion, 



252 SMITH'S ESSAYS 

prevailing customs or habits especially as seen in eastern 
countries, and hundreds of others that might be mentioned; 
but in the long run, the great ocean-level of prices will 
always depend on the quantity of money in use in a given 
domain, as related to the quantity of vendibles found in 
that domain. If while the quantity of money remains 
constant, any considerable proportion of the vendibles in 
any territory decreases in value, the psychologic law re- 
quires that an equal proportion of others shall advance. 

It is evident, furthermore, that owing to the growing 
facilities of communication throughout the world of com- 
merce, prices may be expected everywhere gradually even 
if slowly to approach a common level. 

The first factor to be considered with regard to the 
future of prices is the growth of the ratio of money units 
to units of vendibles; a process that has been steadily 
going on for at least three centuries and bids fair to con- 
tinue for an indefinite time to come. In nearly every 
country we find that men habitually require that their 
money shall perform an ever increasing amount of work 
for each unit, and that a smaller proportion of their own- 
ings shall lie idle in the shape of money. From this cause 
alone, even if the quantity of money and of vendibles 
should remain relatively the same as at present, there 
would be a progressive rise of average prices, as there 
evidently has been from the same cause in the past. 

The second factor is the money or quasi-money based 
wholly on credit, as previously indicated. This is likely to 
prove an even larger factor in the future than it has been 
in the past, by reason of the increasing dissemination of 
banks, unless these institutions can be restricted to the 
loan of their deposits and surplus capital. 



THE PHILOSOPHY OF MONEY 253 

But by far the most important factor, and the one 
probably the most difficult to control, is the increased and 
increasing production of gold. We hive seen that gold 
has been steadily lost to the Western World, at a fairly 
uniform rate per cent, since the year 1600, culminating 
at the present time in a loss of about 1.75 per cent per 
annum of the total gold money stock of the statistical 
world. It now seems very probable that the rate of loss 
in future will be less; but say we place it as high as two 
per cent, a figure much more favorable to the side of 
lower prices and more unfavorable to an advance in 
prices. 

There is today in the gold money stock of the Western 
World in round numbers, about $7,000,000,000. Two 
per cent of this amount is $140,000,000. The annual gold 
production is about $450,000,000. Subtract from this 
sum $140,000,000, the quantity assumed as the annual 
loss at the present time, and we have left $310,000,000 
to be added each year to the money stock of the world. 

Again, insofar as prices depend on gold or are controlled 
by gold, they will continue to rise, other things being 
equal, until the waste of gold each year equals its pro- 
duction. Now $450,000,000 is two per cent of $22,500, 
000,000; and until the gold stock of the world reaches 
that sum, and the waste equals the production, prices 
will continue to rise. 

But we find further that $116,000,000 of silver is now 
annually added to the world's stock of money; that is, if 
we estimate silver on the basis of its coinage value, which 
it would seem that we have a right to do, since this is the 
basis upon which most of it is now, and will likely con- 



254 SMITH'S ESSAYS 

tinue to be used. A silver unit at its present coinage 
relation to gold will likely for a long time in the future, 
buy as much in the East as the corresponding gold unit 
does in the West. 

Uncovered paper is at present added to the money stock 
at the rate of $181,300,000 per annum. This gives a 
total of $657,000,000, added every year to the world's 
money stock. Multiply this by forty, that is, carve 
out for each dollar, forty dollar-worths of vendibles, to 
be taken from the stock already in existence as 
required on the average by our psychological law, and we 
have an apparent annual increase of the world's wealth of 
$26,280,000,000 based wholly on the increase of money. 

If currency were perfectly liquid, and prices did not 
have to adjust themselves by a blind and automatic 
process, they would be found keeping pace strictly with 
the increase of currency, instead of advancing irregularly 
as they now do, and in a way unavoidable under present 
conditions. 

The vast development of industries now going on 
throughout the world will necessarily find employment 
for enormous quantities of money, and this will correspond- 
ingly restrain the rise of prices by increasing the amount 
of vendibles. 

But when we compare the extent of that portion of the 
world already developed, with that which remains to be 
developed, and which may from its own mines, furnish 
more than its proportion of gold, as its development pro- 
ceeds, we cannot well avoid the conclusion that unless 
gold is demonetized or its production materially dimin- 
ished, prices will continue to rise until they reach a level, 



THE PHILOSOPHY OF MONEY 255 

in all probability more than three times as high as at 
present. 

This must inevitr.bly produce a corresponding advance 
in the cost of living with its accompanying hardships, and 
those who deny to labor a corresponding advance in w^ages, 
are building less wisely than they think. 

The Future of Money 

It is becoming clear to the least observant, that rising 
prices and the increased and increasing cost of living, 
constitute the most urgently disturbing fact in current 
history. It would not matter how high prices might go 
if the rise in the price of all things were uniform. What 
could it matter whether a horse cost five dollars or five 
hundred dollars in the paper medium of exchange now 
used, if all other things were valued in proportion, except 
as a matter of arithmetic.^ But if capital holding the 
position of vantage, forces labor to live on a progressively 
smaller portion of its product as prices rise, it requires no 
prophet to foretell the outcome. 

This age of comparative barbarism and racial childhood 
must pass. Gold and silver must be demonetized. What 
then.f^ Will the unfair favoritism that has given to the 
banks almost exclusively the right to issue the paper cur- 
rency continue, or will the people claim and come into 
their own. The issuing of money is a government func- 
tion. It is one of the prerogatives of the people, which 
government has no right to delegate to banks except as 
its agents, whether or not on the deposit of bonds or other 
securities. 



256 SMITH'S ESSAYS 

We are often told how the direct issue of money by 
government has resulted in disastrous inflation; but a 
ready answer to this is found in the fact that this has 
never happened with money having complete function, 
when issued by a stable government. If money has 
gone down with a tottering government, so have bonds 
gone down; and on this ground one had as well say that 
the banks should have the monoply of issuing bonds. 
When an amount of money is issued in any country, just 
sufficient to preserve the ratio of money units to unit- 
worths of vendibles in such country, while at the same 
time the quantity of the unit-worth there is maintained at 
a practical equality with an international standard of 
prices, the difficulty entirely disappears. 

Russia probably today contains a population equal in 
number to that of the entire white race in the time of 
Napoleon, while intercommunication can be more speedily 
effected throughout the civilized world at this time, than 
it could have been in Russia at that period; and yet one 
money suffices throughout Russia. There is no sound 
reason then why gold if not silver should not be demone- 
tized, and no sound reason why the money of the world 
backed by the taxing power and regulated by proper 
treaty stipulations should not be issued by the various 
governments; although the time for this may still be far 
in the future. 

Debasement of the Coinage 

Much has been written by certain historians in depreca- 
tion of the course of various governments in the past, in 



THE PHILOSOPHY OF MONEY 257 

eflFecting what is called debasement of the coinage. The 
instances most frequently cited as a flagrant example, 
are those of the clipping of coins carried on in England 
in the time of Lock and NeT\i:on. 

This was not in any way, however, an act of the govern- 
ment, but was the result of the conduct of private individ- 
uals, and was done in spite of the government. In that 
instance the coins were clipped and the clippings sold 
abroad. A large part of the coinage was thus reduced 
ruinously below the standard required by law and this 
was done so irregularly that confidence was impaired in 
most of the remainder. It was simply a widespread act 
of theft. 

But the recoinage by the governments of most of the 
continental countries was a different matter. The gov- 
ernments there simply called in the coin and issued a 
greater number of small coins or coins containing a larger 
proportion of alloy in their stead. 

This was a boon to the debtor class and worked a hard- 
ship only to the creditor class or the oTvmers of money. 
But then as now, these were the people who could make 
their complaints heard, and who have made them echo 
down the corridors of time. 



MAR 10 1913 



LIBRARY OF CONGRESS 




005 619 940 8 



